Mitigating multicollinearity in ridge regression: a comparative study of quantile-based two parameter weighted KL-estimators

Abstract

In linear regression, when predictors exhibit collinearity, the problem of multicollinearity arises, leading to a reduction in the efficiency of the ordinary least squares (OLS) estimator. In this paper, we develop quantile-based two-parameter ridge weighted Kibria-Lukman (QTPRKL) estimators to address this issue. The proposed QRTRKL estimators are constructed using the eigenvalues of the correlation matrix of predictors. Extensive Monte Carlo simulations are conducted in terms of mean squared error (MSE) criteria to evaluate the performance of the proposed estimators. The results demonstrate that the new QTPRKL0.99 estimator outperforms existing alternatives. Furthermore, the proposed estimator is a generalization of both one and two-parameter ridge estimators and exhibits superior performance compared to OLS. Finally, the effectiveness of the QTPRKL estimators is illustrated using Tobacco dataset, where the findings confirm their superior performance.