New heteroscedasticity-adjusted ridge estimators in linear regression model

Abstract

In ridge regression, we are often concerned with acquiring ridge estimators that lead to the smallest mean square error (MSE). In this article, we have considered the problem of ridge estimation in the presence of multicollinearity and heteroscedasticity. We have introduced a scaling factor which leads to significantly improved performance of the ridge estimators as compared to their classical counterparts. For illustration purposes, we have applied our proposed methodology to some of the popular existing ridge estimators but it can be extended to other estimators as well. We have also compared our proposed estimator with popular existing estimators dealing estimation problem in the same scenario. Extensive simulations reveal the suitability of the proposed strategy, particularly in the presence of severe multicollinearity and heteroscedasticity. A real-life application highlights that the proposed strategy has the potential to be a useful tool for data analysis in the case of collinear predictors and heteroscedastic errors.