Mitigating Multicollinearity in Regression: A Study on Improved Ridge Estimators

Multicollinearity, a critical issue in regression analysis that can severely compromise the stability and accuracy of parameter estimates, arises when two or more variables exhibit correlation with each other. This paper solves this problem by introducing six new, improved two-parameter ridge estimators (ITPRE): NATPR1, NATPR2, NATPR3, NATPR4, NATPR5, and NATPR6. These ITPRE are designed to remove multicollinearity and improve the accuracy of estimates. A comprehensive Monte Carlo simulation analysis using the mean squared error (MSE) criterion demonstrates that all proposed estimators effectively mitigate the effects of multicollinearity. Among these, the NATPR2 estimator consistently achieves the lowest estimated MSE, outperforming existing ridge estimators in the literature. Application of these estimators to a real-world dataset further validates their effectiveness in addressing multicollinearity, underscoring their robustness and practical relevance in improving the reliability of regression models.