Improved Data-Driven Shrinkage Estimators for Regression Models Under Severe Multicollinearity

Multicollinearity is a critical issue in regression analysis, often resulting in inflated variances and unstable parameter estimates. Ridge regression is a widely adopted solution to address this challenge; however, existing ridge estimators are typically tailored to specific scenarios, limiting their universal applicability. Akhtar and Alharthi developed ridge estimators based on condition-adjusted ridge estimators (CAREs) to handle severe multicollinearity issues. However, their approach did not account for the error variances in the estimation process. In this study, we propose improvements to these CAREs by incorporating error variances, resulting in the development of multiscale ridge estimators (MSRE1, MSRE2, MSRE3 and MSRE4) that more effectively address the challenges posed by severe multicollinearity. We compare the performance of our newly proposed estimators with ordinary least square (OLS) and other existing ridge estimators using both simulation studies and real-life datasets. The evaluation, based on estimated mean squared error (MSE), demonstrates that the proposed estimators consistently outperform existing methods, particularly in scenarios with significant multicollinearity, larger sample sizes, and higher predictor dimensions. Results from three real-life datasets further validate the proposed estimators’ ability to reduce estimation error and improve predictive accuracy across diverse practical applications.