Newly Improved Two-Parameter Ridge Estimators: A Better Approach for Mitigating Multicollinearity in Regression Analysis

This study tackles the common issues of multicollinearity arising in regression models due to high correlations among predictor variables, leading to unreliable coefficient estimates and inflated variances, ultimately affecting the model’s accuracy. To address this issue, we introduce four improved two-parameter ridge estimators, named as MIRE1, MIRE2, MIRE3, and MIRE4, which incorporate innovative adjustments such as logarithmic transformations and customized penalization strategies to enhance estimation efficiency. These biased estimators are evaluated through a comprehensive Monte Carlo simulation using the minimum estimated mean square error (MSE) criterion. Although no single ridge estimator performs optimally under all conditions, our proposed estimators consistently outperform existing estimators in most scenarios. Notably, MIRE2 and MIRE3 emerge as the best-performing estimators across a variety of conditions. Their practical utility is further demonstrated through applications to two real-world datasets. The results of the analysis confirm that the proposed ridge estimators offer a reliable and effective approach for improving estimation precision in regression models, as they consistently yield the lowest MSE compared to other estimators.