Robust two-parameter weighted ridge estimators for linear regression models under non-ideal conditions

Simulation and real-life application to show efficiency of the proposed ridge estimator. In linear regression analysis, multicollinearity, heteroscedasticity, and outlier contamination may jointly undermine the performance of the ordinary least squares estimator. These complications often lead to inflated standard errors and distorted statistical inferences. To address these challenges simultaneously, this study proposes a class of adjusted-error-variance two-parameter weighted ridge regression estimators that incorporate robust weights derived from the iterative reweighted least squares algorithm used in M-estimation. Results from Monte Carlo simulations indicate that the proposed estimators consistently outperform their counterparts in achieving the smallest mean square error, particularly across varying degrees of heteroscedasticity, levels of y-directional outlier contamination, and high degrees of correlation among explanatory variables. Additionally, a real-world dataset is analyzed to demonstrate the practical applicability of the proposed estimators.