Modified Liu estimator to address the multicollinearity problem in regression models: A new biased estimation class

Abstract

The multicollinearity problem occurrence of the explanatory variables affects the least-squares (LS) estimator seriously in the regression models. The multicollinearity adverse effects on the LS estimation are also investigated by lots of authors. Also, many biased estimators with one-parameter or two-parameters are developed to overcome this problem. But, the estimators with two-parameter have advantages over that with one-parameter where they have two biasing parameters and at least one of them has the property of handling this problem impact. Therefore, we propose a new modified Liu (MLIU) estimator to handle the multicollinearity of the regression model. Also, we give the necessary and sufficient conditions for the outperforming of the proposed MLIU estimator over the LS, ridge, Liu, Kibria-Lukman (KL), and modified ridge type (MRT) estimators by the known mean squares error criterion. The proposed MLIU estimator biasing parameters are derived by minimizing the known scalar mean square error. Simulations and real data are used to give a good view of the performance of the proposed MLIU estimator. We conclude that the proposed MLIU estimator has the highest performance under almost scenarios using different factors, especially in the cases of severe and high degrees of multicollinearity.