Some Ridge Biasing Parameter for Linear Regression Model and Their Performances on Kibria-Lukman Estimator

Multicollinearity, arising from the violation of the independence assumption among explanatory variables in a linear regression model, poses a significant challenge to parameter estimation. It inflates the variances of the Ordinary Least Squares (OLS) estimates, leading to unstable coefficient estimates and unreliable inference. To mitigate this problem, several biased estimators such as the Ridge and Liu estimators have been developed. Recently, Kibria and Lukman (2020) introduced the Kibria–Lukman Estimator (KLE), a ridge-type alternative designed to improve estimation accuracy under multicollinearity. However, the efficiency of ridge-type estimators critically depends on the choice of the biasing parameter, which controls the trade-off between bias and variance. This study conducts a comprehensive evaluation of 25 existing ridge biasing parameters alongside three newly proposed parameters within the KLE framework. The proposed estimators were assessed using extensive Monte Carlo simulations under varying levels of multicollinearity and sample sizes. Performance was evaluated based on the Mean Squared Error (MSE) criterion. The results reveal that the proposed estimator, Ridge_kgk, consistently outperforms other competing estimators, demonstrating superior efficiency and stability across different data conditions. The findings highlight the potential of the new biasing parameters in enhancing the robustness and predictive accuracy of ridge-type estimators in multicollinearity regression settings.