Development of hybrid ridge–PCA estimators for addressing Multicollinearity in Gaussian linear regression models

This study tackles the persistent issue of multicollinearity in Gaussian linear regression which undermines the efficiency of Ordinary Least Squares (OLS) estimators. While Ridge Regression and Principal Component Analysis (PCA) are common remedies, they have limitations in terms of bias control and interpretability. To address this, the research proposes hybrid Ridge – PCA estimators using four newly developed ridge parameters combined with PCA. A Monte Carlo simulation evaluated 21 estimators including OLS, Ridge, PCA, and Liu estimators under varying sample sizes, error variances and multicollinearity levels using Mean Squared Error (MSE) as the performance metric. Results show that a newly hybrid estimator consistently outperformed other proposed and existing estimators by achieving the lowest MSE. The study demonstrates the strength of integrating regularization with dimensionality reduction to improve regression under multicollinearity.