Comparative Evaluation of Ratio, Regression, and Generalized Regression (GREG) Estimators under Unequal Probability Sampling: A Simulation-Based Study

Abstract: Survey sampling is widely used in official statistics, public health, social sciences, economics, and applied research for estimating population parameters from sample data. The effective use of auxiliary information can improve estimator precision and reduce sampling error, particularly when population structures are complex. This study presents a comparative evaluation of three important estimators in survey sampling: the Ratio Estimator, Regression Estimator, and Generalized Regression (GREG) Estimator. Using simulated finite population data, the study examines estimator performance under repeated sampling conditions. A population dataset was generated using a first-order polynomial relationship between the study variable and an auxiliary variable, allowing assessment under non-proportional population structures. Repeated simulation procedures were applied under unequal probability sampling, and estimator efficiency was evaluated using bias and mean squared error (MSE). The findings indicate that the Ratio Estimator showed reduced efficiency when its proportionality assumption was violated, particularly in the presence of a substantial intercept and skewed auxiliary-variable distribution. The Regression Estimator improved estimation accuracy by incorporating linear adjustment based on auxiliary information. Among the estimators examined, the GREG Estimator demonstrated the highest efficiency, producing the smallest MSE and showing greater robustness under unequal sampling weights. The study highlights the methodological value of calibration-based estimation and supports the use of GREG Estimators in complex survey settings.

Keywords: Auxiliary information, Calibration estimation, Generalized regression estimator, Mean squared error, Survey sampling