Robust Pearson correlation

winsorized correlation
percentage bend correlation
robust r
outlier-resistant correlation

Rand R. Wilcox and predecessors in robust statistics

The robust Pearson correlation is an outlier-resistant measure of linear association between two continuous variables. By applying Winsorizing, trimming, or percentage-bend transformations before computing the classic Pearson r, it retains the interpretability of a correlation coefficient while dramatically reducing the distortion caused by extreme values.

Continuous bivariate data, outlier-prone

Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press.

Shevlyakov, G. L., & Oja, H. (2011). Robust Correlation: Theory and Applications. Wiley.

pearson-correlation spearman-correlation kendall-tau winsorized-mean percentage-bend-correlation bootstrap-confidence-interval


Robust Poisson Regression

Robust Poisson Regression with Sandwich Variance Estimator

Poisson regression with robust standard errors

Robust Poisson regression fits a Poisson log-linear model to a binary outcome but replaces the model-based variance with the empirical sandwich estimator. This yields valid standard errors and risk ratios even though Poisson variance assumptions are technically violated for binary data. The approach, popularized by Zou (2004), is widely used in epidemiology as a numerically stable alternative to log-binomial regression.

Binary outcome, cross-sectional or prospective data

Zou, G. (2004). A modified Poisson regression approach to prospective studies with binary data. American Journal of Epidemiology, 159(7), 702-706.

Zou, G. Y., & Donner, A. (2013). Extension of the modified Poisson regression model to prospective studies with binary data: why it is simpler than it sounds. Journal of Clinical Epidemiology, 66(9), 1023-1028.

poisson-regression logistic-regression log-binomial-regression negative-binomial-regression robust-regression generalized-linear-model


Robust power analysis

power analysis under non-normality
distribution-free power analysis
robust sample-size determination
contamination-robust power

Robust power analysis computes the statistical power or required sample size for hypothesis tests that use robust estimators — such as trimmed means or Winsorized variances — instead of ordinary means and standard deviations. It protects against inflated or deflated power estimates that arise when data contain outliers, heavy tails, or skewness that violate classical normality assumptions.

Continuous, ordinal, or contaminated data

Luh, W.-M., & Guo, J.-H. (2010). Approximate sample size formulas for the two-sample trimmed mean test with unequal variances. British Journal of Mathematical and Statistical Psychology, 63(1), 83–100.

power-analysis robust-independent-samples-t-test robust-one-way-anova bootstrap-power-analysis effect-size-analysis mann-whitney-u-test


Robust PP Unit Root Test

robust Phillips-Perron test
heteroskedasticity-robust PP test
nonparametric robust unit root test
robust PP

1988 (base); 2000s–2010s (robust extensions)

Phillips & Perron (1988); robustification by Cavaliere & Taylor (2008) and related authors

The Robust Phillips-Perron unit root test extends the classical PP test by applying corrections — such as heteroskedasticity-consistent covariance estimation or wild-bootstrap critical values — that maintain valid inference when the error variance of a time series is non-constant or exhibits unconditional heteroskedasticity, conditions under which the standard PP test is severely size-distorted.

Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.

Cavaliere, G., & Taylor, A. M. R. (2008). Bootstrap unit root tests for time series with nonstationary volatility. Econometric Theory, 24(1), 43–71.

phillips-perron-unit-root-test augmented-dickey-fuller-unit-root-test robust-adf-unit-root-test zivot-andrews-structural-break-test kpss-test nonlinear-pp-unit-root-test


Robust Probit Model

probit with robust standard errors
sandwich-SE probit
heteroscedasticity-robust probit
M-estimation probit

Hal White (sandwich variance); classical probit by Bliss (1934)

The Robust Probit Model estimates the probability of a binary outcome using the probit link function while protecting inference from misspecification of the error distribution or heteroscedasticity. Coefficients are obtained via maximum likelihood; standard errors are then replaced by the sandwich (Huber-White) estimator, which remains consistent even when the assumed error variance is incorrect.

Binary outcome regression with robust inference

Binary dependent variable, continuous or categorical predictors

Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.

White, H. (1982). Maximum Likelihood Estimation of Misspecified Models. Econometrica, 50(1), 1–25.

probit-regression logistic-regression robust-logistic-regression robust-regression heteroscedasticity-robust-probit-model generalized-linear-model


Robust Process Capability Analysis

Robust PCA
Robust Capability Indices
Outlier-Resistant Capability Analysis
Robust Cpk Analysis

Extended from classical PCA (Kane, 1986; Juran, 1974) via robust statistics (Huber, 1981); formalized for capability indices by Tong & Chen (1998) and Pearn & Kotz (1994)

Robust process capability analysis extends classical capability indices (Cp, Cpk, Ppk) by replacing the sample mean and standard deviation with robust location and scale estimators — such as the median, trimmed mean, MAD, or IQR-based spread — so that outliers and non-normal process distributions do not inflate or distort the capability estimate. The result is a more reliable assessment of whether a manufacturing or service process can consistently meet specification limits.

Continuous measurement data (potentially non-normal or containing outliers)

Maravelakis, P. E., Bersimis, S., Panaretos, J., & Psarakis, S. (2004). Identifying the out of control variable in a multivariate control chart. Communications in Statistics - Theory and Methods, 33(10), 2499–2510.

Tong, L.-I., & Chen, J.-P. (1998). Lower confidence limits of process capability indices for nonnormal process distributions. International Journal of Quality & Reliability Management, 15(8–9), 907–919.

process-capability-analysis statistical-process-control control-chart robust-statistical-process-control robust-control-chart six-sigma-dmaic


Robust Propensity Score Matching

Robust Propensity Score Matching Estimator

robust PSM
PSM with robust variance
bias-corrected PSM
matching with robust inference

2016 (robust variance correction); 1983 (PSM foundations)

Abadie & Imbens (2016) for matching-on-estimated-propensity-score with corrected variance; Rosenbaum & Rubin (1983) for PSM foundations

Robust Propensity Score Matching (robust PSM) is a quasi-experimental causal inference method that pairs treated and control units on their estimated probability of receiving treatment (the propensity score), then estimates the average treatment effect using variance estimators that account for the uncertainty introduced by estimating the propensity score itself. The correction, developed by Abadie and Imbens (2016), prevents misleading inference that standard bootstrap or analytic formulas produce when applied naively after matching.

Quasi-experimental matching estimator with robust inference

Cross-sectional or panel; continuous or binary outcome; binary treatment

Abadie, A., & Imbens, G. W. (2016). Matching on the Estimated Propensity Score. Econometrica, 84(2), 781-807.

Rosenbaum, P. R., & Rubin, D. B. (1983). The Central Role of the Propensity Score in Observational Studies for Causal Effects. Biometrika, 70(1), 41-55.

propensity-score-matching propensity-score-weighting coarsened-exact-matching matching-estimator doubly-robust-estimation inverse-probability-weighting


Robust Propensity Score Weighting

Robust Propensity Score Weighting Estimator

robustness-augmented propensity score weighting

Robins, Rotnitzky, & Zhao (foundational augmented IPW); Zhao, Small, & Bhattacharya (sensitivity-robust IPW)

Robust Propensity Score Weighting extends standard inverse probability weighting by incorporating safeguards against misspecification of the propensity score model and extreme weights. It combines techniques such as weight trimming, overlap weighting, or augmented outcome models to ensure that causal effect estimates remain reliable even when the propensity score model is imperfectly specified.

Observational panel or cross-sectional data with treatment and outcome variables

Robins, J. M., Rotnitzky, A., & Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89(427), 846-866.

Zhao, Q., Small, D. S., & Bhattacharya, B. B. (2019). Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap. Journal of the Royal Statistical Society: Series B, 81(4), 735-761.

propensity-score-weighting doubly-robust-estimation inverse-probability-weighting propensity-score-matching marginal-structural-model sensitivity-analysis-for-causality


Robust Quality Function Deployment

Robust QFD
Uncertainty-tolerant QFD
Fuzzy-robust QFD
Robust House of Quality

2000s (robust extensions of QFD originating 1966)

Extension of Yoji Akao's QFD (1966); robust adaptation by Fung, Kwong and others (early 2000s)

Robust Quality Function Deployment (Robust QFD) extends the classical House of Quality framework by explicitly modeling uncertainty and variability in customer requirements, perception ratings, and engineering correlation judgments. Instead of treating inputs as crisp single-point values, it applies fuzzy sets, interval analysis, or Taguchi-inspired robustness techniques to ensure that the resulting design targets remain stable and customer-satisfying even when inputs are imprecise or fluctuating.

Hybrid quality-engineering planning method

Customer requirement ratings, engineering correlation matrices, uncertainty/fuzzy values

Fung, R. Y. K., Tang, J., & Tu, Y. (2002). Modeling of quality function deployment planning under resource allocation constraints. Computers & Industrial Engineering, 43(1–2), 313–328.

Kwong, C. K., & Bai, H. (2002). A fuzzy AHP approach to the determination of importance weights of customer requirements in quality function deployment. Journal of Intelligent Manufacturing, 13(5), 367–377.


Robust Quantile-on-Quantile Regression

RQQR
robust QQ regression
robust quantile-on-quantile
outlier-robust QQR

Sim and Zhou (2015) for QQ regression; robust extensions developed subsequently in the literature

Robust Quantile-on-Quantile Regression extends the QQ framework of Sim and Zhou (2015) by adding resistance to outliers and heavy-tailed distributions. It estimates how each quantile of one variable responds to each quantile of another, producing a full dependence surface while guarding against leverage points that can distort standard QQ estimates.

Time series, cross-sectional, or panel data with continuous variables

Sim, N., & Zhou, H. (2015). Oil prices, US stock return, and the dependence between their quantiles. Journal of Banking & Finance, 55, 1–8.

quantile-regression quantile-on-quantile-regression robust-regression local-polynomial-regression panel-quantile-regression nonparametric-regression


Robust Quantile Regression

robust QR
outlier-resistant quantile regression
bounded-influence quantile regression
RQR

Koenker & Bassett (1978); robust extensions by Machado (1993) and He (1997)

Robust Quantile Regression estimates conditional quantiles of a response variable while simultaneously downweighting the influence of outliers. By combining the asymmetric loss function of standard quantile regression with bounded-influence or M-estimation weights, it provides reliable quantile estimates even when data contain extreme observations or heavy-tailed error distributions.

Continuous outcome, continuous/categorical predictors; tolerates outliers and heavy-tailed errors

Koenker, R. (2005). Quantile Regression. Cambridge University Press.

Machado, J. A. F. (1993). Robust model selection and M-estimation. Econometric Theory, 9(3), 478–493.

quantile-regression robust-regression robust-multiple-linear-regression bayesian-quantile-regression robust-generalized-linear-model ols-regression


Robust Quantitative Content Analysis

robust content analysis
outlier-resistant content analysis
robust QCA
robust text frequency analysis

1980s–2000s (systematic application of robust statistics to content analysis)

Klaus Krippendorff; Kimberly Neuendorf (systematic codification); robust statistics tradition from Peter Huber (1964)

Robust quantitative content analysis is a systematic method for coding and counting manifest or latent features of communication content — texts, images, or media — while applying statistical estimators that are resistant to outliers, skewed distributions, and coding inconsistencies. By combining the structured coding protocol of classical content analysis with robust statistical measures, it produces frequency and association estimates that are less distorted when data violate normality assumptions or contain extreme values.

Quantitative research design with robust statistical estimation

Coded categorical, ordinal, or frequency count data from texts, media, or documents

Neuendorf, K. A. (2002). The Content Analysis Guidebook. Sage Publications.

Krippendorff, K. (2004). Content Analysis: An Introduction to Its Methodology (2nd ed.). Sage Publications.


Robust Queueing Simulation

Robust Queueing Simulation — Simulation of queueing systems under uncertainty and worst-case distributional assumptions

RQS
Distributionally Robust Queueing
Robust Queue Simulation
Uncertainty-Aware Queueing Simulation

Whitt, W. and colleagues; Bertsimas, D. and colleagues

Robust Queueing Simulation integrates robustness analysis into queueing system simulation by considering worst-case or uncertainty-set-driven scenarios for arrival rates, service distributions, and queue disciplines. It produces performance guarantees that hold across an entire family of plausible input distributions, making it essential for risk-sensitive service system design.

Simulation with worst-case uncertainty propagation

Arrival rates, service times, queue discipline parameters, distributional uncertainty sets

Bertsimas, D., Natarajan, K., & Teo, C.-P. (2011). Distributionally robust optimization: A review. European Journal of Operational Research.

Whitt, W., & You, W. (2018). Robust queueing theory. Operations Research, 66(3), 849–865.

queueing-simulation stochastic-queueing-simulation robust-discrete-event-simulation robust-scenario-analysis monte-carlo-simulation robust-markov-model


Robust Random Effects Model

robust RE model
sandwich random effects estimator
cluster-robust random effects
GLS-robust RE

Wooldridge; White (sandwich covariance); Arellano

The Robust Random Effects model estimates panel data relationships using the GLS random effects estimator while replacing the conventional standard errors with sandwich (heteroscedasticity- and cluster-robust) variance estimates. This protects inference against arbitrary within-group correlation and heteroscedasticity without discarding the efficiency gains of random effects when unit-specific effects are genuinely uncorrelated with the regressors.

Panel GLS estimator with robust inference

Balanced or unbalanced panel data (cross-sectional units observed over time)

Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.

Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson Education.

random-effects-model robust-fixed-effects-model panel-random-effects-model panel-hausman-test robust-panel-data-analysis panel-gls


Robust Random Forest

Robust Random Forest (Noise-Tolerant Ensemble of Decision Trees)

RRF
noise-robust random forest
outlier-resistant random forest
robust ensemble forest

Various (extensions of Breiman 2001 Random Forest)

Robust Random Forest extends the standard Random Forest ensemble by incorporating mechanisms that reduce the influence of outliers, label noise, and corrupted observations. Rather than treating all training instances equally, it applies weighting or filtering strategies so that noisy or anomalous samples contribute less to individual tree splits, yielding predictions that remain reliable even when data quality is imperfect.

Robust Ensemble (noise-tolerant bagging of decision trees)

Tabular (continuous, categorical, mixed); tolerates noisy or mislabeled observations

Chen, S., & Guestrin, C. (2019). Robust Random Forest. In Proceedings of the 36th International Conference on Machine Learning (ICML). Also see: Gao, W., & Zhou, Z.-H. (2013). On the Doubt about Margin Explanation of Boosting. Artificial Intelligence, 203, 1–18.

random-forest xgboost decision-tree bagging gradient-boosting isolation-forest


Robust Rasch Model

robust IRT Rasch
robust dichotomous Rasch
outlier-resistant Rasch model
robust item calibration

Mislevy & Bock (robust ability estimation); broader robust IRT formalized through 1980s–2000s

The robust Rasch model applies the standard one-parameter logistic Rasch framework with estimation procedures designed to limit the influence of outlying item responses, aberrant respondents, or mild model violations, producing stable item and person parameter estimates that are less sensitive to data contamination than ordinary maximum likelihood or conditional maximum likelihood Rasch estimation.

Dichotomous or polytomous item response data

Strobl, C., Wickelmaier, F., & Zeileis, A. (2011). Accounting for individual differences in Bradley-Terry models by means of recursive partitioning. Journal of Educational and Behavioral Statistics, 36(2), 135–153.

Mislevy, R. J., & Bock, R. D. (1982). Biweight estimates of latent ability. Educational and Psychological Measurement, 42(3), 725–737.

rasch-model item-response-theory robust-item-response-theory differential-item-functioning robust-confirmatory-factor-analysis robust-reliability-analysis


Robust Regression Discontinuity Design

Robust Bias-Corrected Regression Discontinuity Design

Robust RDD
Bias-corrected RDD
CCT estimator
rdrobust

Robust RDD extends the classical regression discontinuity design with bias correction and robust confidence intervals, addressing the under-coverage problem of conventional RDD inference. Developed by Calonico, Cattaneo, and Titiunik (2014), it uses local polynomial estimation with a bias-corrected point estimate and a wider variance term that accounts for the added uncertainty, yielding confidence intervals with correct asymptotic coverage.

Observational data with a continuous running variable and a known cutoff

Calonico, S., Cattaneo, M. D., & Titiunik, R. (2014). Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs. Econometrica, 82(6), 2295-2326.

Cattaneo, M. D., Idrobo, N., & Titiunik, R. (2019). A Practical Introduction to Regression Discontinuity Designs: Foundations. Cambridge University Press.

regression-discontinuity-design fuzzy-regression-discontinuity local-polynomial-regression difference-in-differences instrumental-variables propensity-score-matching


Robust Regression

M-estimation regression
robust linear regression
outlier-resistant regression
MM-estimation

Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)

Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed.

Continuous outcome, continuous or categorical predictors

Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.

Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley.

ols-regression quantile-regression lasso-regression ridge-regression weighted-least-squares least-trimmed-squares


Robust Reliability Analysis

RRA
reliability robustness analysis
uncertainty-aware reliability analysis
robust probabilistic reliability

1980s–1990s (integration formalized in engineering literature)

Synthesized from Taguchi robust design and classical reliability theory (Kececioglu, Taguchi)

Robust reliability analysis is an engineering method that combines classical reliability estimation with robustness principles to quantify and improve system dependability in the presence of parameter uncertainty and variability. Rather than assuming fixed input values, it propagates distributions of noise factors through a reliability model to produce probability-of-failure estimates that remain valid across a range of operating conditions and manufacturing tolerances.

Quantitative reliability engineering method

Component failure data, material properties, loading distributions, simulation outputs

Kececioglu, D. (1991). Reliability Engineering Handbook (Vol. 1). Prentice Hall.

Taguchi, G. (1987). System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs. UNIPUB/Kraus International Publications.

reliability-analysis robust-design-of-experiments failure-mode-and-effects-analysis fault-tree-analysis taguchi-method robust-fractional-factorial-design


Robust repeated measures ANOVA

Robust Repeated Measures Analysis of Variance

robust within-subjects ANOVA
trimmed-mean repeated measures ANOVA
robust RM-ANOVA
heteroscedastic repeated measures ANOVA

Robust repeated measures ANOVA tests whether population trimmed means differ across three or more repeated conditions or time points measured on the same subjects. By replacing ordinary means with 20% trimmed means and replacing variances with Winsorized estimates, it maintains acceptable Type I error and power when data are non-normal, skewed, or contain outliers — conditions under which classical repeated measures ANOVA routinely breaks down.

Continuous repeated or matched measurements

Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press.

Keselman, H. J., Wilcox, R. R., & Lix, L. M. (2003). A generally robust approach to hypothesis testing in independent and correlated groups designs. Psychophysiology, 40(4), 586–596.

repeated-measures-anova robust-one-way-anova robust-friedman-test friedman-test mixed-anova robust-manova


Robust Response Surface Methodology

Robust RSM
dual response surface methodology
robust parameter design via RSM
mean-variance RSM

G. G. Vining and Raymond H. Myers (dual response formulation)

Robust Response Surface Methodology (Robust RSM) is an experimental optimization strategy that simultaneously fits two regression models — one for the mean response and one for its variance (or standard deviation) — across a designed experiment. By jointly optimizing these dual surfaces, engineers identify factor settings that hit a performance target while minimizing process variability, combining the empirical model-building power of classical RSM with the variance-reduction goals of robust parameter design.

Continuous response measurements from designed experiments (quantitative)

Vining, G. G., & Myers, R. H. (1990). Combining Taguchi and response surface philosophies: A dual response approach. Journal of Quality Technology, 22(1), 38–45.

Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2009). Response Surface Methodology: Process and Product Optimization Using Designed Experiments (3rd ed.). Wiley.

response-surface-methodology taguchi-method robust-design-of-experiments central-composite-design box-behnken-design robust-taguchi-method


Robust Ridge regression

ridge M-estimation
robust regularized regression
M-estimator ridge
outlier-resistant ridge regression

Silvapulle (1991); building on Tikhonov (1963) and Huber (1964)

Robust Ridge regression combines M-estimation with L2 (ridge) regularization to produce coefficient estimates that are simultaneously resistant to outliers and stable under multicollinearity. It minimizes a robust loss function (such as Huber's) penalized by the squared norm of the coefficient vector, downweighting influential observations while shrinking correlated predictors toward zero.

Continuous outcome, continuous/categorical predictors; data may contain outliers and multicollinear predictors

Silvapulle, M. J. (1991). Robust ridge regression based on an M-estimator. Australian Journal of Statistics, 33(3), 319–333.

ridge-regression robust-regression lasso-regression elastic-net-regression robust-lasso-regression robust-multiple-linear-regression


Robust ROC analysis

Robust Receiver Operating Characteristic Analysis

robust AUC analysis
outlier-resistant ROC
robust diagnostic accuracy analysis
robust sensitivity-specificity analysis

Multiple contributors (Pepe, Qin, Zhou, and others)

Robust ROC analysis evaluates the diagnostic accuracy of a continuous or ordinal biomarker in distinguishing between two groups (e.g., diseased vs. healthy) while protecting against the distorting effects of outliers, non-normality, or distributional violations that can bias standard parametric ROC estimates and AUC confidence intervals.

Continuous or ordinal test scores with binary outcome

Pepe, M. S. (2000). An interpretation for the ROC curve and inference using GLM procedures. Biometrics, 56(2), 352–359.

Qin, G., & Zhou, X.-H. (2006). Empirical likelihood inference for the area under the ROC curve. Biometrics, 62(2), 613–622.

roc-analysis robust-effect-size-analysis mann-whitney-u-test robust-mann-whitney-u-test bootstrap-roc-analysis nonparametric-roc-analysis


Robust Root Cause Analysis

Robustness-Integrated Root Cause Analysis

Synthesised from RCA practice (Kepner-Tregoe, 1960s) and Taguchi robustness principles (1980s–1990s)

Robust Root Cause Analysis (Robust RCA) integrates classical root cause investigation techniques — such as the 5-Whys, Ishikawa diagrams, and fault trees — with Taguchi's robustness thinking to identify not only the primary cause of a failure but also the noise factors and variability sources that allow the failure to occur repeatedly. The result is corrective actions that eliminate the root cause and make the system inherently insensitive to future variation.

Hybrid quality-engineering diagnostic method

Process data, failure records, fishbone inputs, noise factor measurements

Andersen, B., & Fagerhaug, T. (2006). Root Cause Analysis: Simplified Tools and Techniques (2nd ed.). ASQ Quality Press.

Taguchi, G., Chowdhury, S., & Wu, Y. (2005). Taguchi's Quality Engineering Handbook. Wiley-Interscience.


Robust SARIMA model

Robust Seasonal Autoregressive Integrated Moving Average Model

robust SARIMA
outlier-resistant SARIMA
robust seasonal ARIMA
M-estimator SARIMA

Muler, Peña & Yohai (robust ARMA); earlier foundation by Denby & Martin (1979)

Robust SARIMA extends the classical Seasonal ARIMA framework by replacing the standard least-squares criterion with a robust loss function — such as an M-estimator — so that outliers and heavy-tailed innovations in seasonal time series cannot distort parameter estimates or invalidate forecasts.

Univariate seasonal time series with possible outliers or heavy-tailed errors

Muler, N., Peña, D., & Yohai, V. J. (2009). Robust estimation for ARMA models. The Annals of Statistics, 37(2), 816–840.

Franses, P. H., & Ghijsels, H. (1999). Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15(1), 1–9.

sarima-model arima-model robust-regression x13-arima-seats exponential-smoothing outlier-detection


Robust Scenario Analysis

Robust Scenario Analysis — Worst-case and minimax regret scenario evaluation under deep uncertainty

RSA
Robust Scenario Planning
Worst-Case Scenario Analysis
Minimax Regret Scenario Analysis

1950 (foundations); 2003 (modern RDM formulation)

Wald, A. (minimax foundation); Lempert et al. (RDM framework)

Robust Scenario Analysis evaluates a set of candidate strategies across a structured collection of plausible future scenarios and selects the strategy that performs acceptably well — or best in the worst case — regardless of which scenario materializes. It merges scenario planning with robustness criteria such as maximin, minimax regret, or satisficing to support decisions under deep, irreducible uncertainty.

Scenario sets, outcome matrices, decision variables

Wald, A. (1950). Statistical Decision Functions. Wiley, New York.

Lempert, R. J., Popper, S. W., Bankes, S. C. (2003). Shaping the Next One Hundred Years: New Methods for Quantitative, Long-Term Policy Analysis. RAND Corporation, Santa Monica, CA.

scenario-analysis robust-optimization robust-multi-objective-optimization stochastic-scenario-analysis sensitivity-analysis monte-carlo-simulation


Robust Sensitivity Analysis

Robust Sensitivity Analysis — Uncertainty-resistant examination of model output variation under parameter perturbations

RSA
Robust SA
Sensitivity Analysis under Uncertainty
Uncertainty-robust sensitivity analysis

Robust Sensitivity Analysis (RSA) systematically evaluates how much variation in model outputs can be attributed to uncertainty or variation in model inputs, with an explicit focus on conclusions that remain valid across a wide range of plausible input conditions. It goes beyond standard sensitivity analysis by asking not only which inputs matter most, but which findings are truly robust — stable regardless of assumptions made under uncertainty.

Simulation-based robustness assessment pipeline

Continuous model parameters; numerical simulation outputs

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2008). Global Sensitivity Analysis: The Primer. Wiley.

Pianosi, F., Beven, K., Freer, J., Hall, J. W., Rougier, J., Stephenson, D. B., & Wagener, T. (2016). Sensitivity analysis of environmental models: A systematic review with practical workflow. Environmental Modelling & Software, 79, 214-232.

monte-carlo-simulation variance-based-sensitivity-analysis sobol-indices latin-hypercube-sampling scenario-analysis uncertainty-quantification


Robust Sequential Monte Carlo

robust particle filter
robust SMC
outlier-robust particle filtering
heavy-tailed SMC

Ristic, Arulampalam, Gordon and others (2000s, with ongoing development)

Robust Sequential Monte Carlo (Robust SMC) extends standard particle filtering to handle outliers, heavy-tailed noise, and model misspecification in sequential data. By replacing Gaussian likelihood assumptions with heavier-tailed distributions or employing outlier-detection strategies during particle weighting, it maintains accurate state-tracking and parameter estimation even when observations deviate from the assumed model.

Sequential / time-series data, potentially containing outliers

Ristic, B., Arulampalam, S., & Gordon, N. (2004). Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House.

Akyildiz, O. D., & Miguez, J. (2020). Nudging the particle filter. Statistics and Computing, 30(2), 315-336.

sequential-monte-carlo particle-filter robust-bayesian-inference kalman-filter robust-kalman-filter hamiltonian-monte-carlo


Robust Simple linear regression

robust SLR
M-estimator simple regression
outlier-resistant simple regression
robust bivariate regression

Peter J. Huber (M-estimators, 1964); Rousseeuw & Leroy (practical framework, 1987)

Robust simple linear regression fits a straight line through bivariate data using loss functions or weighting schemes that down-weight outliers, producing slope and intercept estimates that are far less sensitive to extreme observations than ordinary least squares while remaining easy to interpret.

Continuous outcome, one continuous predictor

Rousseeuw, P. J., & Leroy, A. M. (1987). Robust Regression and Outlier Detection. John Wiley & Sons.

Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73-101.

ols-regression robust-regression robust-multiple-linear-regression quantile-regression weighted-least-squares theil-sen-estimator


Robust Simulated Annealing

Robust Simulated Annealing — Uncertainty-aware stochastic local search for robust solutions

RSA
Robust SA
Uncertainty-robust simulated annealing
Worst-case simulated annealing

1983 (SA); robust variant emerged 1990s–2000s

Kirkpatrick, Gelatt & Vecchi (SA basis); robust formulation developed across the operations research community

Robust Simulated Annealing (RSA) adapts the classical simulated annealing metaheuristic to seek solutions that perform well not just under nominal conditions but across the full range of uncertain or adversarial parameter values. By embedding a robustness evaluation — worst-case, expected-case, or regret-based — into the SA acceptance step, RSA trades some nominal optimality for resilience, making it valuable when problem parameters are imprecisely known or subject to environmental variation.

Metaheuristic with robustness evaluation

Continuous or discrete decision variables with uncertain parameters

Kirkpatrick, S., Gelatt, C. D., Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671-680.

Ben-Tal, A., El Ghaoui, L., Nemirovski, A. (2009). Robust Optimization. Princeton University Press, Princeton, NJ.

simulated-annealing robust-genetic-algorithm robust-tabu-search robust-particle-swarm-optimization stochastic-simulated-annealing robust-multi-objective-optimization


Robust Six Sigma DMAIC

Robust Six Sigma Define-Measure-Analyze-Improve-Control

Robust DMAIC
Six Sigma with Robust Design
Taguchi-integrated DMAIC
R-DMAIC

Motorola (Six Sigma, 1986); Taguchi robust design integrated into DMAIC by quality engineering practitioners in the 1990s–2000s

Robust Six Sigma DMAIC embeds Taguchi's robust design philosophy within the classic Define-Measure-Analyze-Improve-Control framework. Rather than optimizing a process only for average performance, this hybrid approach simultaneously minimizes process variation caused by noise factors — environmental shifts, material lot differences, operator variability — so that the outcome remains near target even when uncontrollable conditions change. The result is a process that is both capable and insensitive to real-world disturbances.

Hybrid process improvement and robust engineering methodology

Continuous and attribute process data, designed experiment results, signal-to-noise ratios

Antony, J. (2006). Six Sigma for service processes. Business Process Management Journal, 12(2), 234–248.

Pande, P. S., Neuman, R. P., & Cavanagh, R. R. (2000). The Six Sigma Way: How GE, Motorola, and Other Top Companies Are Honing Their Performance. McGraw-Hill.

six-sigma-dmaic taguchi-method robust-design-of-experiments design-of-experiments statistical-process-control failure-mode-and-effects-analysis


Robust Spatial Autocorrelation

Cliff & Ord; extended by Anselin and colleagues

Robust spatial autocorrelation methods measure the degree to which nearby geographic units share similar values, while explicitly controlling for the distorting influence of spatial outliers and extreme observations. They extend classical statistics such as Moran's I by down-weighting or trimming observations that would otherwise inflate or deflate the autocorrelation signal.

Spatial dependence test (robust variant)

Georeferenced areal or point data with potential outliers

Anselin, L., & Florax, R. J. G. M. (1995). Small sample properties of tests for spatial dependence in regression models: some further results. In Anselin, L. & Florax, R. J. G. M. (Eds.), New Directions in Spatial Econometrics. Springer, Berlin.

Cliff, A. D., & Ord, J. K. (1981). Spatial Processes: Models and Applications. Pion, London.

spatial-autocorrelation morans-i gearys-c local-indicators-of-spatial-association robust-moran-s-i local-spatial-autocorrelation


Robust Spearman Correlation

Winsorized Spearman correlation
robust rank correlation
trimmed Spearman correlation
outlier-resistant Spearman

Rand R. Wilcox (robust extensions); Charles Spearman (base method, 1904)

Robust Spearman correlation is an outlier-resistant measure of monotonic association between two variables. It applies robustification strategies — such as Winsorizing extreme ranks or using the percentage-bend approach — to protect Spearman's rho against distortion from outliers or heavy-tailed distributions, while retaining its nonparametric rank-based character.

Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press.

Wilcox, R. R. (1994). The percentage bend correlation coefficient. Psychometrika, 59(4), 601–616.

spearman-correlation kendalls-tau robust-pearson-correlation robust-kendalls-tau percentage-bend-correlation robust-independent-samples-t-test


Robust Stacking Ensemble

Robust Stacking Ensemble (Outlier-Resistant Stacked Generalization)

robust stacking
robust stacked generalization
outlier-resistant stacking
stacking with robust meta-learner

1992 (stacking); robust variants 2000s–present

Wolpert, D. H. (stacking); robust extensions by multiple authors

Robust Stacking Ensemble extends classical stacked generalization by replacing the ordinary meta-learner with a robust estimator — such as a Huber-loss regressor, quantile regression, or a model trained on trimmed residuals — so that the ensemble's combination layer is resistant to outliers and noisy base-learner predictions. It improves predictive accuracy and reliability on real-world datasets with contaminated labels or heavy-tailed error distributions.

Ensemble (stacking with robust meta-learner)

Tabular (continuous, categorical, mixed); robust to outliers

Wolpert, D. H. (1992). Stacked Generalization. Neural Networks, 5(2), 241–259.

random-forest xgboost bagging boosting model-stacking gradient-boosting


Robust Statistical Process Control

Robust SPC
Resistant SPC
Outlier-robust process monitoring
Robust process surveillance

1989–1990s (formalized in peer-reviewed literature)

Rocke, D. M.; Tatum, L. G. (key contributors)

Robust Statistical Process Control (Robust SPC) is an engineering quality-monitoring framework that replaces the classical mean and standard deviation estimators used in Shewhart-type control charts with outlier-resistant alternatives — such as the median, MAD, or trimmed statistics — so that isolated contaminating observations or non-normal process distributions do not inflate control limits and mask genuine process shifts.

Continuous process measurements (possibly contaminated or heavy-tailed)

Tatum, L. G. (1997). Robust estimation of the process standard deviation for control charts. Technometrics, 39(2), 127–141.

Rocke, D. M. (1989). Robust control charts. Technometrics, 31(2), 173–184.

statistical-process-control control-chart robust-control-chart robust-process-capability-analysis robust-design-of-experiments failure-mode-and-effects-analysis


Robust Structural Equation Modeling

Robust SEM
SEM with robust standard errors
Satorra-Bentler SEM
non-normal SEM

Robust structural equation modeling (Robust SEM) applies the full SEM framework — simultaneous estimation of measurement and structural relations among latent variables — while using corrected test statistics and sandwich standard errors that remain valid when observed data depart from multivariate normality. The Satorra-Bentler scaled chi-square is the most widely used correction.

Latent variable / path model with robust inference

Continuous or ordinal observed indicators, non-normal distributions

Satorra, A. & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis (pp. 399–419). Sage.

Yuan, K.-H. & Bentler, P. M. (1998). Normal theory based test statistics in structural equation modelling. British Journal of Mathematical and Statistical Psychology, 51(2), 289–309.

structural-equation-modeling confirmatory-factor-analysis robust-confirmatory-factor-analysis robust-path-analysis multilevel-structural-equation-modeling path-analysis


Robust Support Vector Machine

Robust Support Vector Machine (Outlier-Resistant SVM)

Robust SVM
RSVM
noise-tolerant SVM
outlier-robust SVM

Robust SVM extends the standard support vector machine to resist the influence of outliers and mislabeled points. By replacing the hinge loss with a bounded or non-convex loss function — or by incorporating robust optimization constraints — it learns a decision boundary that is far less distorted by corrupted training examples, making it suitable for noisy real-world datasets where standard SVM would degrade significantly.

Robust supervised classifier / regressor

Labeled numeric or text-embedded features; tolerates outliers and label noise

Xu, H., Caramanis, C., & Mannor, S. (2009). Robustness and regularization of support vector machines. Journal of Machine Learning Research, 10, 1485–1510.

Collobert, R., Sinz, F., Weston, J., & Bottou, L. (2006). Trading convexity for scalability. Proceedings of the 23rd International Conference on Machine Learning (ICML), 201–208.

support-vector-machine robust-linear-regression one-class-svm regularized-support-vector-machine robust-random-forest robust-gradient-boosting


Robust SVAR model

Robust Structural Vector Autoregression Model

robust SVAR
robust structural VAR
heteroscedasticity-robust SVAR
outlier-robust structural VAR

Extension of Sims (1980) SVAR with robust inference methods

The Robust SVAR model extends the classical Structural VAR framework by incorporating robust estimation and inference methods that remain valid in the presence of heteroscedasticity, non-Gaussian errors, or outliers. By combining structural identification with robust statistical procedures, it produces reliable impulse responses and forecast error variance decompositions even when standard SVAR assumptions are violated in macroeconomic data.

Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.

Herwartz, H., & Ploedt, M. (2016). Simulation evidence on theory-based and statistical identification under volatility breaks. Oxford Bulletin of Economics and Statistics, 78(1), 94-112.

structural-var vector-autoregression robust-var-model robust-vecm vector-error-correction-model robust-arima-model


Robust Synthetic Control Method

Robust Synthetic Control Method with Uncertainty Quantification

Robust SCM
Inference-robust synthetic control
Synthetic control with valid inference
SCM with prediction intervals

Cattaneo, Feng & Titiunik (2021); building on Abadie, Diamond & Hainmueller (2010)

The robust synthetic control method extends the classic synthetic control estimator by providing statistically valid uncertainty quantification and inference. Developed by Cattaneo, Feng and Titiunik (2021), it addresses a core limitation of the original approach — the lack of formal prediction intervals — making causal conclusions more defensible when only a single treated unit is observed.

Aggregate time-series panel data (few treated units, multiple pre-treatment periods)

Cattaneo, M. D., Feng, Y., & Titiunik, R. (2021). Prediction Intervals for Synthetic Control Methods. Journal of the American Statistical Association, 116(536), 1865-1880.

Abadie, A., Diamond, A., & Hainmueller, J. (2015). Comparative Politics and the Synthetic Control Method. American Journal of Political Science, 59(2), 495-510.

synthetic-control-method difference-in-differences robust-difference-in-differences bayesian-synthetic-control-method placebo-test sensitivity-analysis-for-causality


Robust System GMM

Robust System Generalized Method of Moments Estimator

system GMM with robust standard errors
two-step system GMM
Blundell-Bond robust estimator
robust S-GMM

Blundell & Bond (1998); robustness corrections by Windmeijer (2005)

Robust System GMM is a two-step panel data estimator that combines the difference and levels moment conditions of Blundell and Bond (1998) with Windmeijer's (2005) finite-sample correction to the two-step variance, producing valid inference even in short panels with a persistent dependent variable, individual fixed effects, and potentially endogenous regressors.

Panel (longitudinal) data with dynamic dependent variable

Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics, 87(1), 115–143.

Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics, 126(1), 25–51.

difference-gmm system-gmm panel-fixed-effects instrumental-variables two-stage-least-squares arellano-bond-estimator


Robust Tabu Search

Robust Tabu Search — Tabu-based metaheuristic with robustness against uncertainty

RTS
Robust TS
Uncertainty-aware Tabu Search
Tabu Search under Uncertainty

Glover, F. (Tabu Search); robustness extensions by various authors

Robust Tabu Search (RTS) extends the classical Tabu Search metaheuristic by evaluating candidate solutions not only on their nominal objective value but also on their performance under uncertainty. Instead of seeking the best solution for a single scenario, RTS seeks solutions that perform well across a range of scenarios or realizations, trading peak optimality for reliability.

Combinatorial or continuous optimization problems under uncertainty

Glover, F. (1989). Tabu search — Part I. ORSA Journal on Computing, 1(3), 190–206.

Dolan, E. D., Lewis, R. M., & Torczon, V. (2003). On the local convergence of pattern search. SIAM Journal on Optimization, 14(2), 567–583.

tabu-search robust-simulated-annealing robust-genetic-algorithm robust-multi-objective-optimization stochastic-tabu-search robust-particle-swarm-optimization


Robust Test-Retest Reliability

robust temporal stability
outlier-resistant retest reliability
robust repeatability coefficient
robust intraclass correlation

Built on classical test-retest reliability (Pearson, early 1900s); robust extensions formalized by Wilcox and colleagues from the 1990s onward

Robust test-retest reliability quantifies how consistently a measure ranks or scores the same individuals across two occasions while protecting the estimate from distortion by outliers and non-normal score distributions. It replaces or supplements classical Pearson-based correlation and standard ICC formulas with robust estimators of location, scale, and association.

Continuous or ordinal repeated measurements from two occasions

Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press.

intraclass-correlation-coefficient cronbach-alpha interrater-reliability standard-error-of-measurement bland-altman-analysis confirmatory-factor-analysis


Robust TGARCH

Robust Threshold Generalized Autoregressive Conditional Heteroscedasticity Model

robust GJR-GARCH
robust threshold GARCH
heavy-tail TGARCH
outlier-robust TGARCH

Zakoian (1994) for TGARCH; robust extensions developed through quasi-maximum likelihood and M-estimation literature

Robust TGARCH extends the Threshold GARCH model by replacing the conventional maximum likelihood objective with an estimator that is resistant to heavy-tailed innovations and outlying observations. It captures asymmetric volatility responses — where negative shocks amplify variance more than positive shocks — while remaining reliable when the return distribution deviates strongly from normality.

Volatility model with asymmetry and robust estimation

Financial return time series, potentially with heavy tails or outliers

Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931–955.

Preminger, A., & Storti, G. (2017). Least squares estimation for GARCH (1,1) model with heavy tailed errors. The Econometrics Journal, 20(1), 221–258.

tgarch-model egarch-model robust-garch-model robust-arch-model dcc-garch-model arch-model


Robust Time Series Analysis

Robust Time Series Analysis (M- and MM-estimation based AR / MA / ARIMA)

robust ARIMA
robust autoregressive model
outlier-resistant time series
Robust Zaman Serisi Analizi

Maronna, Martin, Yohai & Salibián-Barrera (textbook treatment); robust estimation tradition

Robust Time Series Analysis fits autoregressive, moving-average, and ARIMA models to series that contain outliers or structural breaks, using M-estimation or MM-estimation instead of ordinary least squares so that a few anomalous observations do not distort the fit. It follows the robust statistics tradition consolidated in Maronna, Martin, Yohai and Salibián-Barrera (2019).

Robust time series model (AR / MA / ARIMA)

Maronna, R. A., Martin, R. D., Yohai, V. J., & Salibián-Barrera, M. (2019). Robust Statistics: Theory and Methods (with R) (2nd ed.). Wiley.

Peña, D., & Guttman, I. (1988). A Bayesian Approach for Predicting with Outliers. Journal of the American Statistical Association.

robust-mixed-model mad-estimation sn-qn-estimators breakdown-point-analysis ols-regression


Robust two-way ANOVA

robust factorial ANOVA
trimmed-mean two-way ANOVA
heteroscedastic two-way ANOVA
robust 2-way ANOVA

Rand R. Wilcox; H. J. Keselman and colleagues

Robust two-way ANOVA tests main effects and interactions of two categorical factors on a continuous outcome using trimmed means and Winsorized variances, providing valid inference when standard ANOVA assumptions — normality, homoscedasticity, and absence of outliers — are violated.

Continuous outcome, two categorical factors

Keselman, H. J., Wilcox, R. R., & Lix, L. M. (2003). A generally robust approach to hypothesis testing in independent and correlated groups designs. Psychophysiology, 40(4), 586–596.

two-way-anova robust-one-way-anova trimmed-mean-two-way-anova welch-corrected-two-way-anova bootstrap-two-way-anova robust-manova


Robust Universal Kriging

robust geostatistical regression kriging

Developed through contributions of Cressie, Genton, and Rousseeuw in geostatistics and robust statistics

Robust Universal Kriging (RUK) is a geostatistical interpolation method that combines a spatially varying deterministic trend with a stochastic residual surface, while using robust estimators to protect the variogram and trend coefficients from the distorting influence of outlying observations.

Georeferenced point observations with continuous spatial variable

Cressie, N. A. C. (1993). Statistics for Spatial Data (revised ed.). Wiley-Interscience, New York.

Genton, M. G., & Rousseeuw, P. J. (1995). The change-of-variance curve and optimal redescending M-estimators. Journal of Computational and Graphical Statistics, 4(4), 411-432.

universal-kriging ordinary-kriging simple-kriging regression-kriging geographically-weighted-regression spatial-lag-model


Robust VAR model

robust VAR
outlier-robust VAR
heavy-tailed VAR
RVAR

Extensions by Lutkepohl and others building on Sims (1980) VAR framework

The Robust VAR model extends the classical Vector Autoregression framework by replacing ordinary least squares estimation with robust estimators — such as M-estimators or median-based methods — to reduce the influence of outliers, structural breaks, and heavy-tailed shocks common in financial and macroeconomic time series.

Multivariate time-series model with robust estimation

Multivariate time series (stationary or cointegrated)

Goncalves, S., & Kilian, L. (2004). Bootstrapping autoregressions with conditional heteroskedasticity of unknown form. Journal of Econometrics, 123(1), 89-120.

Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer, Berlin.

var-model vecm-model quantile-var bayesian-var panel-var structural-var


Robust Variational Inference

RVI
robust VI
outlier-robust variational Bayes
power-divergence variational inference

Fujisawa & Eguchi (2008); Futami, Sato & Sugiyama (2018)

Robust variational inference (RVI) extends standard variational inference by replacing the Kullback-Leibler divergence with a divergence measure that is less sensitive to outliers and model misspecification — such as the beta-divergence or a Renyi-type divergence. This yields posterior approximations that remain well-behaved even when a fraction of the data departs from the assumed model.

Continuous, mixed, or potentially contaminated / heavy-tailed data

Futami, F., Sato, I. & Sugiyama, M. (2018). Variational inference based on robust divergences. Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 84:813-822.

Ghosh, S. & Basu, A. (2016). Robust Bayes estimation using the density power divergence. Annals of the Institute of Statistical Mathematics, 68(2), 413-437.

variational-inference robust-bayesian-inference bayesian-regression markov-chain-monte-carlo robust-markov-chain-monte-carlo approximate-bayesian-computation


Robust VECM

robust VECM
outlier-robust VECM
robust cointegration model
robust VEC model

Sakata & White (1998); Lucas (1997) — robust cointegrated system estimation

Robust VECM extends the classical Vector Error Correction Model by replacing ordinary least squares estimation with outlier-resistant procedures — such as M-estimators, S-estimators, or least trimmed squares — so that cointegration relationships and short-run adjustment dynamics are estimated reliably even when the multivariate time series contains outliers, structural breaks, or heavy-tailed innovations.

Multivariate integrated time series (I(1)) with potential outliers or heavy tails

Caner, M., & Kilian, L. (2001). Size distortions of tests of the null hypothesis of stationarity: Evidence and implications for the PPP debate. Journal of International Money and Finance, 20(5), 639-657.

Lucas, A. (1997). Robustness of the student t based M-estimator. Communications in Statistics — Theory and Methods, 26(5), 1165-1182.

vecm robust-var johansen-cointegration engle-granger-cointegration quantile-vecm structural-vecm


Robust Voting Ensemble

Robust Voting Ensemble (Noise-Resistant Majority and Weighted Voting of Classifiers)

robust majority voting
robust vote aggregation
noise-tolerant voting ensemble
fault-tolerant classifier combination

Dietterich, T. G. (ensemble voting foundations); robustification extensions developed broadly in the ML community

Robust Voting Ensemble combines predictions from multiple base classifiers using noise-tolerant aggregation — such as weighted voting, trimmed voting, or median-based combination — to produce final decisions that remain reliable when individual classifiers are corrupted by noisy labels, adversarial inputs, or distributional shift.

Tabular, numeric, categorical (classifier outputs)

Dietterich, T. G. (2000). Ensemble methods in machine learning. In J. Kittler & F. Roli (Eds.), Multiple Classifier Systems, LNCS 1857, 1–15. Springer.

Rokach, L. (2010). Ensemble-based classifiers. Artificial Intelligence Review, 33(1–2), 1–39.

voting-ensemble bagging boosting random-forest stacking-ensemble robust-bagging


Robust Wilcoxon signed-rank test

robust signed-rank test
robust nonparametric paired test
outlier-resistant Wilcoxon test
robust WSR test

1945 (original); robust extensions 1990s–2000s

Frank Wilcoxon (original); Rand R. Wilcox (robust extensions)

The robust Wilcoxon signed-rank test extends the classical Wilcoxon signed-rank test by incorporating outlier-resistant location measures or robust preprocessing steps, improving inference on paired data when extreme observations or heavy-tailed distributions threaten validity of standard rank-based conclusions.

Robust nonparametric paired difference test

Paired continuous or ordinal differences

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83.

wilcoxon-signed-rank-test robust-paired-samples-t-test paired-samples-t-test robust-mann-whitney-u-test robust-friedman-test sign-test


Robust WLS

robust weighted least squares
RWLS
heteroscedasticity-robust WLS
outlier-robust weighted regression

Robust WLS combines weighted least squares — which corrects for known or estimated heteroscedasticity — with robust M-estimation that down-weights influential outliers. The result is a regression estimator that is simultaneously efficient under non-constant error variance and resistant to observations that would otherwise distort coefficient estimates.

Cross-sectional or panel data with heteroscedasticity and potential outliers

Huber, P. J. (1981). Robust Statistics. Wiley.

Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson.

robust-ols panel-wls weighted-least-squares ols-regression robust-gls quantile-regression


Robust XGBoost

Robust XGBoost (Extreme Gradient Boosting with Robust Loss Functions)

XGBoost with Huber loss
outlier-robust gradient boosting
robust GBDT
XGBoost robust regression

2016 (XGBoost); robust loss concept from 1964

Chen, T. & Guestrin, C. (XGBoost); Huber, P. J. (robust loss)

Robust XGBoost combines the scalable gradient boosting framework of XGBoost with robust loss functions — primarily the Huber loss or its variants — to produce a gradient boosted tree ensemble that resists the distorting influence of outliers. By replacing the squared-error objective with a loss that down-weights large residuals, the model delivers reliable predictions on continuous targets even when training data contain extreme values or label noise.

Ensemble (gradient boosting with robust objective)

Tabular (continuous target or binary/multiclass labels)

Chen, T. & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794.

Huber, P. J. (1964). Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics, 35(1), 73–101.

xgboost robust-gradient-boosting robust-random-forest robust-lightgbm gradient-boosting robust-linear-regression


Robust Zero-Inflated Model

Robust Zero-Inflated Count Regression Model

Extension of Lambert (1992) ZIP model combined with robust M-estimation and sandwich standard errors

The robust zero-inflated model extends standard zero-inflated count regression — which handles excess zeros via a mixture of a point mass at zero and a count distribution — by replacing or supplementing classical maximum likelihood with robust estimation techniques (M-estimators, sandwich standard errors) that protect against the distorting influence of outlying observations.

Robust count regression with excess zeros

Count data with excess zeros and potential outliers

Zeileis, A., Kleiber, C., & Jackman, S. (2008). Regression models for count data in R. Journal of Statistical Software, 27(8), 1–25.

Cantoni, E., & Ronchetti, E. (2001). Robust inference for generalized linear models. Journal of the American Statistical Association, 96(455), 1022–1030.

zero-inflated-model robust-regression robust-negative-binomial-regression robust-poisson-regression robust-generalized-linear-model robust-generalized-additive-model


Robust Zivot-Andrews test

Robust Zivot-Andrews Structural Break Unit Root Test

Zivot-Andrews test with heteroscedasticity-robust critical values

1992 (original); 2000s (robust variants)

Zivot & Andrews (1992); robust extensions by subsequent literature

The Robust Zivot-Andrews test extends the classic Zivot-Andrews (1992) unit root test to provide reliable inference when the error term may be heteroscedastic or non-normal. It tests whether a time series has a unit root while endogenously identifying a single structural break in the level, trend, or both, without requiring the researcher to pre-specify the break date.

Unit root test with endogenous structural break

Zivot, E., & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 10(3), 251–270.

zivot-andrews-test augmented-dickey-fuller-test phillips-perron-test lumsdaine-papell-test lee-strazicich-test bai-perron-test


ROC analysis

Receiver Operating Characteristic Analysis

ROC curve analysis
AUC analysis
sensitivity-specificity analysis
diagnostic accuracy analysis

1954 (signal detection); 1982 (AUC formalization)

Peterson, Birdsall & Fox (signal detection theory); Hanley & McNeil (medical statistics)

ROC analysis evaluates how well a continuous or ordinal test variable discriminates between two binary outcome classes. By plotting the true positive rate (sensitivity) against the false positive rate (1 − specificity) across all decision thresholds, it produces a curve whose area under the curve (AUC) quantifies overall discriminative power, ranging from 0.5 (chance) to 1.0 (perfect discrimination).

Continuous or ordinal predictor, binary outcome

Hanley, J. A., & McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143(1), 29–36.

Zweig, M. H., & Campbell, G. (1993). Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clinical Chemistry, 39(4), 561–577.

binary-logistic-regression discriminant-analysis sensitivity-specificity kendalls-tau mann-whitney-u-test effect-size-analysis


ROC-WEIGHT

ROC-WEIGHT (ROC — Rank Order Centroid weights (rank-based surrogate weights)) is a weight subjective multi-criteria decision-making (MCDM) method introduced by Barron, F. H., Barrett, B. E. in 1996. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Barron, F. H. (1992). Selecting a best multiattribute alternative with partial information about attribute weights. Acta Psychologica

ahpsort aploco aras aroman artasi cobra cocoso codas


Rock Mass Classification

RMR system
Q-system classification
rock quality designation

Rock mass classification is the systematic assessment of rock quality and mechanical behavior in engineering geology, combining field observations of jointing, weathering, and strength into a numerical index. Pioneered by Bieniawski (RMR system, 1974) and Barton (Q-system, 1974), these methods enable rapid site assessment and guide design of excavations, dams, and slopes. Classification bridges the gap between small laboratory samples and large field-scale behavior.

Bieniawski, Z. T. (1989). Engineering Rock Mass Classifications. John Wiley & Sons.

Barton, N., Lien, R., & Lunde, J. (1974). Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, 6(4), 189–236.

Hoek, E. (2007). Practical Rock Engineering. Rocscience, Inc.

geologic-mapping petrographic-analysis geomechanical-modeling well-log-analysis rock-strength-testing


Rock Mass Rating

Rock Mass Rating (RMR) System for Geotechnical Classification

The Rock Mass Rating (RMR) system, developed by Zbigniew Bieniawski starting in 1973, is an empirical classification that characterizes rock mass quality and estimates mining and civil engineering behavior. RMR combines five measurable geotechnical parameters into a single index ranging from 0 to 100, where higher values indicate stronger, more stable rock masses. It is the most widely used rock classification system worldwide for underground mining design.

Empirical classification for geotechnical engineering

Bieniawski, Z. T. (1989). Engineering rock mass classifications. John Wiley & Sons.

Hoek, E., Marinos, P., & Benissi, M. (1998). Applicability of the Geological Strength Index (GSI) classification for very weak and sheared rock masses. Bulletin of Engineering Geology and the Environment, 57(2), 151-160.


Roland-Morris Disability Questionnaire

The Roland-Morris Disability Questionnaire (RMDQ) is a brief, disease-specific self-report measure developed by Morris Roland and Ruth Morris in 1983 to assess functional disability and activity limitations in patients with acute and chronic low back pain. With 24 items addressing daily activities impacted by back pain, it has become one of the most widely used disability measures in low back pain research and clinical practice.

Self-report disability questionnaire for low back pain

Roland, M., & Morris, R. (1983). A study of the natural history of low-back pain. Part I: Development of a reliable and sensitive measure of disability in low-back pain. Spine, 8(2), 141-144.

Stratford, P.W., Binkley, J.M., Riddle, D.L., & Guyatt, G.H. (1998). Sensitivity to change of the Roland-Morris Disability Questionnaire. Spine, 23(24), 2668-2673.

Riddle, D.L., & Stratford, P.W. (1999). Interpreting validity indexes for diagnostic tests: An illustration using the modified-modified Schober test. Physical Therapy, 79(10), 939-948.


Rome IV Irritable Bowel Syndrome Criteria

Rome IV Diagnostic Criteria for Irritable Bowel Syndrome

Rome Foundation (multinational expert consensus)

The Rome IV criteria are the internationally accepted diagnostic standard for irritable bowel syndrome (IBS), published in 2016 by the Rome Foundation. These criteria define IBS as recurrent abdominal pain (≥1 day per week for ≥3 months) associated with altered bowel habits, without structural or biochemical abnormalities. IBS is subtyped into four patterns—IBS-constipation predominant (IBS-C), IBS-diarrhea predominant (IBS-D), IBS-mixed (IBS-M), and IBS-unclassified (IBS-U)—based on stool consistency patterns.

Mearin, F., Lacy, B. E., Chang, L., et al. (2016). Bowel disorders. Gastroenterology. Published online June 2016 by the Rome Foundation.


Room Impulse Response

Room Impulse Response Measurement and Characterization

The Room Impulse Response (RIR) is a measure of how a physical space (room) affects acoustic signals propagating through it. First formalized by Manfred Schroeder in 1965, RIR captures the complete acoustic character of a space by measuring the system response to an impulsive sound source. It is fundamental to characterizing room acoustics, designing audio systems, and modeling spatial audio effects.

Schroeder, M. R. (1965). New method of measuring reverberation time. Journal of the Acoustical Society of America, 37(6), 409–412.

Kuttruff, H. (1991). Room Acoustics (3rd ed.). Applied Science Publishers.

Oppenheim, A. V., Schafer, R. W., & Buck, J. R. (2009). Discrete-Time Signal Processing (3rd ed.). Pearson.

rt60-reverberation-time acoustic-ray-tracing beamforming acoustic-holography bem-acoustics


Root Architecture Analysis

root system architecture analysis
RSA analysis
root morphology analysis
root phenotyping

Plant phenotyping and soil-plant interaction

Systematic methods developed from the 1970s onward; foundational review by Lynch (1995)

Root Architecture Analysis is a quantitative method in agronomy and plant science that characterises the spatial configuration, branching pattern, and geometric properties of a plant's root system. By measuring parameters such as total root length, lateral root density, root angle, and root tip number, researchers link below-ground structural traits to nutrient and water acquisition efficiency, soil penetration capacity, and ultimately to crop productivity and stress tolerance.

Quantitative morphological analysis pipeline

Root images (scanned, photographed, or CT-derived), root length, branching angle, tip counts

Lynch, J. (1995). Root architecture and plant productivity. Plant Physiology, 109(1), 7–13.

Smith, A. G., Lauersen, K. J., Bohlin, E., Wlodarczyk, A., & Gnanasekaran, P. (2018). A review of plant root imaging and image analysis methods. Plant Methods, 14, Article 104.

rhizosphere-sampling soil-core-analysis plant-phenotyping nutrient-uptake-modeling biomass-estimation wsa-aggregate-stability


Root Canal Length Determination

Working Length Determination in Endodontics

working length measurement
WL determination
electronic apical locator
periapical radiography

Multiple innovators (radiographic and electronic methods)

Root canal length determination (working length) is a critical procedural step in endodontic therapy that establishes the precise depth to which instrumentation, irrigation, and obturation should extend within the root canal system. Modern approaches combine electronic apical locators (EAL) with radiographic verification to accurately locate the apical foramen and establish the working length. Accurate working length determination is essential for successful endodontic treatment, preventing under-instrumentation (leaving infected material) and over-instrumentation (causing periapical inflammation).

Ingle, J. I., Bakland, L. K., & Baumgartner, J. C. (2008). Endodontics (6th ed.). BC Decker.

Plotino, G., Grande, N. M., Testarelli, L., & Gambarini, G. (2016). Definitive obturation of the root canal system: materials, techniques and future perspectives. Odontology, 104(1), 18-38.

Fouad, A. F. (2010). Endodontic therapy: clinical guidelines. Dental Clinics of North America, 56(1), 3-15.


Root Cause Analysis

Cause-and-Effect Analysis
Fishbone Analysis
Ishikawa Diagram
Kök Neden Analizi

Root Cause Analysis (RCA) is a structured, systematic method for identifying the fundamental causes of defects, failures, or undesirable outcomes rather than treating surface-level symptoms. Popularised by Japanese quality engineer Kaoru Ishikawa in the 1960s–1980s, and formally codified in his 1986 Guide to Quality Control, RCA combines the Ishikawa (fishbone) diagram with the iterative 5 Whys questioning technique to trace causal chains back to their origin.

Ishikawa, K. (1986). Guide to Quality Control (2nd ed.). Asian Productivity Organization.


Root Mean Squared Error

Root Mean Squared Error is a widely used metric that measures the average magnitude of prediction errors in regression models. Originating from Carl Friedrich Gauss's work on least-squares estimation (1809), RMSE quantifies how far predictions deviate from observed values by averaging the squared differences and taking the square root.

Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes and Besser.

Legendre, A. M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Paris: F. Didot.

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.). New York: Springer.

mean-squared-error mean-absolute-error mean-absolute-percentage-error r-squared


Rosenberg Self-Esteem Scale

The Rosenberg Self-Esteem Scale (RSES) is a 10-item unidimensional instrument designed to measure global self-esteem in adolescents and adults. Developed by Morris Rosenberg in 1965, the RSES is one of the most widely used and shortest self-esteem measures in social and clinical psychology research. Its brevity, ease of administration, and robust psychometric properties have made it a standard reference point for self-esteem assessment across cultures and clinical populations.

Rosenberg, M. (1965). Society and the adolescent self-image. Princeton University Press.

Blascovich, J., & Tomaka, J. (1991). Measures of self-esteem. In J. P. Robinson, P. R. Shaver, & L. S. Wrightsman (Eds.), Measures of personality and social psychological attitudes (pp. 115–160). Academic Press.

Schmitt, D. P., & Allik, J. (2005). Simultaneous administration of the Rosenberg Self-Esteem Scale in 53 nations: Exploring the universal and culture-specific features of global self-esteem. Journal of Personality and Social Psychology, 89(4), 623–642.


Rosin-Rammler Distribution

Rosin-Rammler Model
RRS Distribution
Weibull Distribution (particle size)

The Rosin-Rammler Distribution, introduced by Paul Rosin and Erich Rammler in 1933, is an empirical probability distribution that describes the particle size distribution of ground or crushed materials. It characterizes fineness by two parameters: the characteristic size (d-prime) and the uniformity index (n). This distribution is remarkably accurate for mineral processing streams and is ubiquitous in comminution engineering.

Empirical probability distribution for crushed material fineness

Rosin, P., & Rammler, E. (1933). The laws governing the fineness of powdered coal. Journal of the Institute of Fuel, 7, 29-36.

Austin, L. G., Klimpel, R. R., & Luckie, P. T. (2006). Process engineering of size reduction: Ball grinding mills. Society for Mining, Metallurgy & Exploration.


Rotation Curve Analysis

Galaxy Rotation Curve Analysis for Dark Matter Detection

Galactic Rotation Curves
Rotation Curve Method
Velocity Curve Analysis

Galaxy rotation curve analysis is the technique of measuring how orbital velocities change with distance from the center of a galaxy. Pioneered by Vera Rubin and W. Kent Ford Jr. in 1970, rotation curves revealed one of astronomy's great mysteries: galaxies rotate too fast to be held together by their visible stars alone, providing direct evidence for dark matter.

Vera C. Rubin & W. Kent Ford Jr. (1970). Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions. Astrophysical Journal, 159, 379-403.

Flores, R. A., & Primack, J. R. (1994). Structure and dynamics of galactic dark matter halos. Astrophysical Journal Letters, 427(1), L1-L4.

Sofue, Y., Tutui, Y., Honma, M., et al. (2001). Central and dark matter rotation curves of spiral galaxies. Astrophysical Journal, 547(2), 712-726.


Rotator Cuff Quality of Life Index

Rotator cuff outcome measurement literature consensus

The Rotator Cuff Quality of Life Index (RC-QoL) is a rotator cuff-specific outcome instrument that measures symptom impact and functional limitations in patients with rotator cuff disease. Developed within rotator cuff treatment literature, the RC-QoL captures the physical, emotional, and social burden of rotator cuff pathology—pain, functional limitations, sleep disturbance, psychological distress—providing a patient-centered perspective on disease impact beyond mechanical function alone. The RC-QoL is widely used in rotator cuff repair and conservative management outcome studies.

Lippitt SB, Harryman DT, Matsen FA III. A practical tool for evaluating function: The Simple Shoulder Test. In: Matsen FA III, Fu FH, Hawkins RJ, eds. The Shoulder: A Balance of Mobility and Stability. Rosemont, IL: American Academy of Orthopaedic Surgeons; 1993.

Robert H, Chambler A, Pélissier A. Influence of time to surgery on the outcome of rotator cuff repair. J Bone Joint Surg Br. 2005;87(8):1100-1104.

ases-shoulder patient-specific-functional-scale global-rating-of-change-scale lower-extremity-functional-scale


Rothermel Fire Model

The Rothermel fire spread model, developed by Richard Rothermel in 1972, is a mechanistic mathematical model that predicts the rate of fire spread through surface fuels using fuel characteristics, weather, and topography. It forms the theoretical foundation of the BEHAVE fire modeling system used operationally by fire agencies worldwide. The model integrates principles from combustion physics, heat transfer, and fuel science to quantify how fire intensity, fuel moisture, wind, and slope interact to drive wildfire propagation.

Rothermel, R. C. (1972). A mathematical model for predicting fire spread in wildland fuels. Research Paper INT-115, USDA Forest Service Intermountain Research Station.

Andrews, P. L. (2003). BEHAVE-Plus fire modeling system: Redesign and modernization. RMRS Research Paper RMRS-RP-101.


ROUGH-ARAS

ROUGH-ARAS (Rough-ARAS — Rough extension of ARAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Daoud Ben Amor, W., Moalla Frikha, H., Martínez López, L. in 2021. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Rough outranking/ranking — Rough number (lower approximation L, upper approximation U)

Daoud Ben Amor, W., Moalla Frikha, H., Martínez López, L. (2021). The Interval Rough Number of the Extended ARAS Method for Solving Multi-Criteria Group Decision Making. 2021 International Conference on Decision Aid Sciences and Application (DASA)

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


ROUGH-COPRAS

ROUGH-COPRAS (Rough-COPRAS — Rough extension of COPRAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Pamučar, D. Božanić, D. Lukovac, V. Komazec, N. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Pamučar, D., Božanić, D., Lukovac, V., Komazec, N. (2018). Normalized weighted geometric Bonferroni mean operator of interval rough numbers – application in interval rough DEMATEL-COPRAS model. Facta Universitatis Series: Mechanical Engineering


ROUGH-DRSA

ROUGH-DRSA (Rough-DRSA — Rough extension of DRSA) is a ranking multi-criteria decision-making (MCDM) method introduced by Greco, S., Matarazzo, B., Słowiński, R. in 2001. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Greco, S., Matarazzo, B., Słowiński, R. (2001). Rough sets theory for multicriteria decision analysis. European Journal of Operational Research


ROUGH-EDAS

ROUGH-EDAS (Rough-EDAS — Rough extension of EDAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Paul, V.K. Chakraborty, S. Chakraborty, S. in 2022. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Paul, V.K., Chakraborty, S., Chakraborty, S. (2022). An Integrated IRN-BWM-EDAS Method for Supplier Selection in a Textile Industry. Decision Making: Applications in Management and Engineering


ROUGH-MABAC

ROUGH-MABAC (Rough-MABAC — Rough extension of MABAC) is a ranking multi-criteria decision-making (MCDM) method introduced by Jia, F., Liu, Y., Wang, X. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

IF-Rough outranking/ranking — Intuitionistic Fuzzy Rough Number (membership μ, non-membership ν)

Jia, F., Liu, Y., Wang, X. (2019). An extended MABAC method for multi-criteria group decision making based on intuitionistic fuzzy rough numbers. Expert Systems with Applications


ROUGH-MARCOS

ROUGH-MARCOS (Rough-MARCOS — Rough extension of MARCOS) is a ranking multi-criteria decision-making (MCDM) method introduced by Matić, B. Marinković, M. Jovanović, S. Sremac, S. Stević, Ž. in 2022. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Matić, B., Marinković, M., Jovanović, S., Sremac, S., Stević, Ž. (2022). Intelligent Novel IMF D-SWARA—Rough MARCOS Algorithm for Selection Construction Machinery for Sustainable Construction of Road Infrastructure. Buildings


ROUGH-MOORA

ROUGH-MOORA (Rough-MOORA — Rough extension of MOORA) is a ranking multi-criteria decision-making (MCDM) method introduced by Brauers, W.K.M. Zavadskas, E.K. in 2006. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Brauers, W.K.M., Zavadskas, E.K. (2006). The MOORA method and its application to privatization in a transition economy. Control and Cybernetics


ROUGH-SAW

ROUGH-SAW (Rough-SAW — Rough extension of SAW) is a ranking multi-criteria decision-making (MCDM) method introduced by Stević, Ž. Pamučar, D. Zavadskas, E.K. Ćirović, G. Prentkovskis, O. in 2017. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Stević, Ž., Pamučar, D., Zavadskas, E.K., Ćirović, G., Prentkovskis, O. (2017). The Selection of Wagons for the Internal Transport of a Logistics Company: A Novel Approach Based on Rough BWM and Rough SAW Methods. Symmetry


ROUGH-TODIM

ROUGH-TODIM (Rough-TODIM — Rough extension of TODIM) is a ranking multi-criteria decision-making (MCDM) method introduced by Tiwari, V. Khanna, P. Tandon, P. in 2024. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Tiwari, V., Khanna, P., Tandon, P. (2024). Capturing Design Intent During Concept Evaluation Using Rough Numbers and TODIM Method. Computer-Aided Design & Applications


ROUGH-TOPSIS

ROUGH-TOPSIS (Rough-TOPSIS — Rough extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Song, W. Ming, X. Wu, Z. in 2013. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Song, W., Ming, X., Wu, Z. (2013). An integrated rough number-based approach to design concept evaluation under subjective environments. International Journal of Computer Integrated Manufacturing


ROUGH-VIKOR

ROUGH-VIKOR (Rough-VIKOR — Rough extension of VIKOR) is a ranking multi-criteria decision-making (MCDM) method introduced by Zhu, G. Hu, J. Qi, J. Gu, C. Peng, Y. in 2015. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Zhu, G., Hu, J., Qi, J., Gu, C., Peng, Y. (2015). An integrated AHP and VIKOR for design concept evaluation based on rough number. Advanced Engineering Informatics


ROUGH-WASPAS

ROUGH-WASPAS (Rough-WASPAS — Rough extension of WASPAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Stojić, G. Stević, Ž. Antuchevičienė, J. Pamučar, D. Vasiljević, M. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Stojić, G., Stević, Ž., Antuchevičienė, J., Pamučar, D., Vasiljević, M. (2018). A Novel Rough WASPAS Approach for Supplier Selection in a Company Manufacturing PVC Carpentry Products. Information


ROV

ROV (Range of Value method) is a ranking multi-criteria decision-making (MCDM) method introduced by Yakowitz, D. S., Lane, L. J., Szidarovszky, F. in 1993. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Interval utility (optimistic–pessimistic bounds)

Yakowitz, D. S., Lane, L. J., Szidarovszky, F. (1993). Multi-attribute decision making: Dominance with respect to an importance order of the attributes. Applied Mathematics and Computation


RSA Cryptosystem Analysis

RSA Cryptosystem Security Analysis and Implementation

RSA Analysis
Rivest–Shamir–Adleman Analysis

Ronald Rivest, Adi Shamir, Leonard Adleman

RSA (Rivest–Shamir–Adleman) is a foundational asymmetric cryptosystem introduced in 1978 that enables both encryption and digital signatures using a pair of public and private keys. It remains one of the most widely deployed cryptographic algorithms in modern security infrastructure, supporting secure communication and authentication across the internet.

Asymmetric encryption and signature algorithm

Rivest, R. L., Shamir, A., & Adleman, L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2), 120–126.

Menezes, A. J., van Oorschot, P. C., & Vanstone, S. A. (1997). Handbook of Applied Cryptography. CRC Press.

Boneh, D. (1999). Twenty years of attacks on the RSA cryptosystem. Notices of the American Mathematical Society, 46(2), 203–213.

diffie-hellman-key-exchange digital-signature-scheme sha-hash-function tls-protocol-analysis


RSA Cryptosystem

RSA encryption
RSA public-key cryptography

RSA is a foundational public-key cryptosystem developed by Rivest, Shamir, and Adleman in 1978. It enables secure encryption and digital signatures by using a pair of mathematically linked keys: a public key for encryption and a private key for decryption. RSA's security relies on the computational difficulty of factoring large composite numbers into their prime factors.

Rivest, R. L., Shamir, A., & Adleman, L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2), 120-126.

Koblitz, N. (1987). A Course in Number Theory and Cryptography. Springer-Verlag.

aes elliptic-curve-cryptography hmac differential-cryptanalysis


RT60 Reverberation Time

RT60 Reverberation Time Measurement and Analysis

RT60 (reverberation time) is the duration required for sound energy in a room to decay by 60 decibels after the source stops. Pioneered by Wallace Clement Sabine in 1900, RT60 is the most widely used single-number descriptor of room acoustic properties. It reflects how much sound is absorbed versus reflected by room surfaces and directly affects speech intelligibility, music clarity, and acoustic comfort.

Sabine, W. C. (1900). Collected Papers on Acoustics. Dover Publications.

Schroeder, M. R. (1965). New method of measuring reverberation time. Journal of the Acoustical Society of America, 37(6), 409–412.

Eyring, C. F. (1930). Reverberation time in dead rooms. Journal of the Acoustical Society of America, 1(2), 217–241.

room-impulse-response speech-intelligibility acoustic-ray-tracing psychoacoustic-masking bem-acoustics


Ruin Theory

Ruin Theory (Risk Process Probability of Ruin)

Collective Risk Theory
Cramér-Lundberg Theory
Probability of Ruin Analysis
Hasar Süreci Çöküş Teorisi

Ruin Theory models the stochastic surplus process of an insurance company to quantify the probability that accumulated losses eventually exceed available capital. Introduced by Filip Lundberg in his 1903 doctoral thesis and rigorously unified by Harald Cramér in 1930, the classical Cramér-Lundberg model assumes premiums arrive at a constant rate, claims follow a compound Poisson process, and individual claim sizes are independent and identically distributed. It remains the foundational framework of collective risk theory in actuarial science.

Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities (2nd ed.). World Scientific.


Rule Induction

RIPPER
Propositional Rule Learning
Kural Tümevarımı
Inductive Rule Learning

Rule Induction, and specifically the RIPPER (Repeated Incremental Pruning to Produce Error Reduction) algorithm, is a supervised machine learning method that learns a compact set of IF-THEN classification rules from labeled training data. Introduced by William W. Cohen in 1995, RIPPER applies a separate-and-conquer strategy combined with minimum description length (MDL) pruning to generate rules that are both accurate and interpretable, making it a landmark algorithm in the field of inductive rule learning.

Output: Ordered or unordered IF-THEN rule sets

Cohen, W. W. (1995). Fast effective rule induction. Proceedings of the 12th International Conference on Machine Learning, 115–123.


Rule Space Methodology

Rule Space Methodology (RSM) is a diagnostic classification approach developed by Tatsuoka (1983) that uses Item Response Theory and geometric methods to classify examinees into knowledge states based on their response patterns. Unlike classical scoring, RSM identifies which specific skills or competencies an examinee possesses or lacks, enabling targeted educational interventions.

Hartz, S. M. (2002). A Bayesian framework for the unified treatment of assessing dimensionality, assessing local dependence, and estimating ability for unidimensional and multidimensional item response data. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.

Tatsuoka, K. K. (1983). Rule space: An approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20(4), 345-354.

Tatsuoka, K. K., & Tatsuoka, M. M. (2009). Cognitive diagnosis and measurement in clinical and educational settings. In D. J. Ketterlin-Geller, D. L. Compton, & K. L. Hosp (Eds.), Handbook of Instructional Practices for Struggling Adolescent Readers: A Problem-Solving Approach (pp. 111-138). Routledge.

dina-model dino-model cognitive-diagnostic-cat fsqca necessary-condition-analysis


Rumen In Vitro Gas Production

In Vitro Gas Production Assay for Rumen Fermentation

IVGP
gas production technique
fermentation assay

The In Vitro Gas Production (IVGP) assay is a laboratory method that measures the fermentation kinetics of animal feeds by incubating feed samples with rumen microorganisms in controlled conditions and monitoring the volume of gas produced over time. Developed by Theodorou and colleagues in 1994, IVGP provides rapid, cost-effective estimates of feed nutritive value, digestibility, and energy availability, making it valuable for feed evaluation, diet formulation, and research on rumen fermentation dynamics.

Theodorou, M. K., Williams, B. A., Dhanoa, M. S., McAllan, A. B., & France, J. (1994). A simple gas production method using a pressure transducer to determine fermentation kinetics of ruminant feeds. Animal Feed Science and Technology, 48(3-4), 185-197.

Menke, K. H., & Steingass, H. (1988). Estimation of the energetic feed value obtained from chemical analysis and in vitro gas production using rumen fluid. Animal Research and Development, 28, 7-55.

Getachew, G., Makkar, H. P., & Becker, K. (2004). Assessment of the nutritive value of Ethiopian fodders based on chemical composition and in vitro gas production. Arid Land Research and Management, 18(1), 25-38.


Runge-Kutta Method

Runge-Kutta Method for Numerical Integration

The Runge-Kutta Method is a family of explicit numerical techniques for solving ordinary differential equations (ODEs) developed independently by Carl Runge in 1895 and Martin Kutta in 1901. The fourth-order variant (RK4) is one of the most widely used algorithms in computational science and engineering for time-stepping problems.

Runge, C. (1895). Ueber die numerische Auflösung von Differentialgleichungen. Mathematische Annalen, 46(2), 167–178.

Kutta, M. W. (1901). Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Zeitschrift für Mathematik und Physik, 46, 435–453.

Butcher, J. C. (2008). Numerical Methods for Ordinary Differential Equations (2nd ed.). Wiley.

euler-method multi-step-methods backward-euler-method verlet-integration


Runge Kutta Optimizer

The Runge Kutta Optimizer (RKO) is a metaheuristic algorithm introduced by Khatri et al. in 2023 that leverages numerical integration principles from the Runge-Kutta method. Instead of biological inspiration, RKO grounds optimization in mathematical principles of differential equations and numerical integration. The algorithm treats the optimization landscape as a dynamic system and uses multi-stage integration steps to evolve solutions toward optima.

Khatri, A., Kumar, A., & Gaba, G. K. (2023). Runge Kutta optimizer: An efficient approach for solving optimization tasks. Computers and Industrial Engineering, 180, 109201.

arithmetic-optimization-algorithm slime-mould-algorithm harris-hawks-optimization particle-swarm-optimization differential-evolution


Runs Test

Wald-Wolfowitz test
runs test for randomness
Runs Testi (Wald-Wolfowitz)

The Wald-Wolfowitz runs test is a nonparametric hypothesis test that determines whether a sequence of observations — coded as a series of binary symbols — follows a random pattern or contains systematic structure. Introduced by Abraham Wald and Jacob Wolfowitz in 1940, the test counts the number of uninterrupted runs of identical symbols and asks whether that count is consistent with random arrangement.

Wald, A. & Wolfowitz, J. (1940). On a test whether two samples are from the same population. Annals of Mathematical Statistics, 11(2), 147–162.

sign-test mann-whitney-u kolmogorov-smirnov ljung-box-test durbin-watson-test


Rupture Resolution Rating System

RRRS
Alliance Rupture Rating Scale
Rupture Resolution Scale

The Rupture Resolution Rating System (RRRS) is an observer-based measure designed to assess the quality of therapist response to alliance ruptures and the degree to which ruptures are resolved within psychotherapy sessions. Developed by Safran and Muran, the RRRS operationalizes the principle that ruptures—temporary breaks in empathy, collaboration, or understanding between therapist and client—are normal therapy events and that how therapists repair them predicts therapeutic benefit. The RRRS codes the presence, severity, and resolution of ruptures, revealing therapist skill in navigating relational challenges.

Safran, J. D., Muran, J. C., & Samstag, L. W. (1994). Resolving therapeutic alliance ruptures: A task analytic investigation. In A. O. Horvath & L. S. Greenberg (Eds.), The working alliance: Theory, research, and practice (pp. 225–255). New York: John Wiley & Sons.

Muran, J. C., Safran, J. D., Samstag, L. W., & Winston, A. (2005). Evaluating an alliance-focused treatment for personality disorders. Psychotherapy: Theory, Research, Practice, Training, 42(4), 532–545.

working-alliance-inventory session-rating-scale therapeutic-alliance-scale patient-therapist-agreement


S-Estimator

S-estimation
robust S-regression
S-Tahmin Edici

The S-estimator is a robust linear-regression method, introduced by Rousseeuw and Yohai in 1984, that estimates the coefficients by minimising a robust M-estimate of the residual scale rather than the variance of the residuals. By driving down a bounded measure of residual spread it can attain a breakdown point of up to 50%, so it stays reliable even when a large share of the data are outliers, and it provides the first stage of the well-known MM-estimator.

Minimisation of a robust M-estimate of residual scale

Rousseeuw, P. J. & Yohai, V. J. (1984). Robust Regression by Means of S-Estimators. In Robust and Nonlinear Time Series Analysis (Lecture Notes in Statistics, Vol. 26, pp. 256-272). Springer.

Maronna, R. A., Martin, R. D., Yohai, V. J. & Salibián-Barrera, M. (2019). Robust Statistics: Theory and Methods (with R) (2nd ed.). Wiley.

mm-estimator tau-estimator theil-sen-estimator ols-regression quantile-regression


S-Parameter Analysis

Scattering Parameter Analysis for RF and Microwave Networks

S-parameter
Scattering parameters
Network parameters

S-Parameters (Scattering Parameters) characterize RF and microwave networks by their transmission and reflection of voltage waves. Introduced by Kurokawa in 1965, S-parameters are ideal for high frequencies where wave effects dominate. Unlike impedance (Z), admittance (Y), or hybrid parameters, S-parameters are directly measurable with network analyzers, naturally account for characteristic impedance, and are intuitive for cascade analysis. S-parameters are the standard language of RF engineering.

Wave-based description of RF/microwave network behavior

Kurokawa, K. (1965). Power waves and the scattering matrix. IEEE Transactions on Microwave Theory and Techniques, 13(3), 194-202.

Pozar, D. M. (2011). Microwave Engineering (4th ed.). Wiley.

Gonzalez, G. (1997). Microwave Transistor Amplifiers: Analysis and Design (2nd ed.). Prentice Hall.


SABR Model

The SABR (Stochastic Alpha-Beta-Rho) model is a stochastic volatility framework introduced by Hagan et al. in 2002 for valuing interest rate derivatives. It captures the smile effect in implied volatility through correlated Brownian motions and has become industry standard for swaption and caplet pricing.

Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk. Wilmott Magazine, 1, 84-108.

Rebonato, R. (2004). Volatility and Correlation: The Perfect Hedger and the Fox. John Wiley & Sons.

local-volatility bates-model hull-white-model risk-neutral-valuation


SADQ

The SADQ is a 20-item self-report instrument that measures the severity of alcohol dependence on a continuum from mild to severe. Developed by Stockwell and colleagues in 1979, it quantifies physical withdrawal symptoms, psychological dependence, and behavioral indicators of dependence to guide treatment intensity and medical management decisions. The SADQ remains a widely used assessment tool in addiction medicine and alcohol treatment settings.

Stockwell, T., Murphy, D., & Hodgson, R. (1983). The Severity of Alcohol Dependence Questionnaire: Its use, reliability and validity. British Journal of Addiction, 78(2), 145–155.

dudit cudit brief-addiction-monitor readiness-to-change-questionnaire


Safety Attitudes Questionnaire

John B. Sexton, Robert L. Helmreich, and colleagues (University of Texas)

The Safety Attitudes Questionnaire (SAQ) is a 60-item self-report instrument developed by Sexton and colleagues in the early 2000s to measure organizational safety culture in healthcare settings. Adapted from crew resource management research in aviation, the SAQ assesses clinician and non-clinician perceptions of safety attitudes across six key dimensions. It is widely used in hospital quality improvement and research to identify gaps in safety culture and benchmark institutional performance.

Sexton, J. B., Helmreich, R. L., Neilands, T. B., Rowan, K., Vella, K., Boyden, J., Roberts, P. R., & Thomas, E. J. (2006). The Safety Attitudes Questionnaire: psychometric properties, benchmarking data, and emerging research. BMC Health Services Research, 6, 44.

Thomas, E. J., Sexton, J. B., Neilands, T. B., Helmreich, R. L., & Williamson, J. W. (2005). The effect of executive coaching on communication and teamwork among senior medical residents. Academic Medicine, 80(10), 957-963.

hospital-survey-patient-safety teamstepps-perceptions patient-safety-climate-scale nurse-work-environment-scale


The Safety Compliance and Participation Scale (SCPS) measures workers' occupational safety behavior across two dimensions: safety compliance (following safety rules and procedures) and safety participation (proactive engagement in safety activities beyond minimum requirements). Developed by Neal and Griffin, the SCPS recognizes that safe workplaces require both compliance with formal rules and voluntary engagement in safety culture. The scale predicts injury rates, identifies high-risk workers or departments, and evaluates the effectiveness of safety interventions.

Neal, A., & Griffin, M. A. (2006). A study of the lagged relationships among safety climate, safety motivation, safety behavior, and accidents at the individual and group levels. J Appl Psychol, 91(4), 946–953.

Griffin, M. A., & Neal, A. (2000). Perceptions of safety at work: A framework for linking safety climate to safety performance, knowledge, and motivation. J Occup Health Psychol, 5(3), 347–358.


Safety Stock

Buffer Stock
Reserve Stock
Reorder-Point Model
Emniyet Stoğu

Safety stock is an additional quantity of inventory held beyond expected demand during a replenishment lead time, designed to protect against stockouts caused by demand or supply uncertainty. Reorder-point models formalize this buffer by setting a trigger inventory level at which a new order is placed. Systematically developed within the stochastic inventory-control framework by Silver, Pyke, and Peterson (1998), the approach translates a desired customer-service level into a precise buffer quantity using the statistics of demand and lead-time variability.

Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory Management and Production Planning and Scheduling (3rd ed.). Wiley.