Generalized kibria-lukman estimator for multicollinearity in linear regression models: theoretical insights and comparative analysis

Multicollinearity, a common issue in regression models caused by high correlations among explanatory variables, undermines the stability and reliability of traditional estimators like Ordinary Least Squares (OLS). This study investigates the Generalized Kibria-Lukman (GKL) estimator, introduced by Dawoud et al. (2022), which uses a flexible biasing parameter to address the inflated variances typical in multicollinear datasets. Through comprehensive simulation studies and empirical testing, we compare the GKL estimator’s performance with other biased estimators, including ridge regression and the Liu estimator, focusing on Mean Squared Error (MSE) as the primary evaluation metric. The results demonstrate that the GKL estimator consistently achieves lower MSE values, particularly in highly multicollinear conditions, underscoring its effectiveness as a robust alternative for improving accuracy in regression models where traditional methods struggle. These findings highlight the GKL estimator’s potential as a superior choice in complex, multicollinear regression environments.