The robustified Liu-type estimator for low- and high-dimensional data

Abstract

Liu-type estimators are a widely used family of shrinkage estimators designed to address the multicollinearity problem in regression models. However, when the normality assumption is violated, shrinkage estimators become distorted and provide misleading results. In such cases, robust estimators are often preferred. This paper introduces a new robustified Liu-type estimator, which is resistant to vertical outliers and leverage points in low-dimensional data, and extends this approach to high-dimensional data as well. The proposed estimators combine the advantages of shrinkage and robust estimators, offering both high robustness and protection against the detrimental effects of multicollinearity. To demonstrate the performance of the newly proposed estimators, simulation studies and real data examples are conducted. The results show that the robustified Liu-type estimator outperforms traditional estimators in most scenarios, based on the mean squared error (MSE) criterion, for both low- and high-dimensional data.