Handling multicollinearity and outliers using weighted ridge least trimmed squares

Abstract

Common problems in multiple linear regression models are multicollinearity and outliers. In this paper, we will propose a robust ridge regression. It is based on weighted ridge least trimmed squares (WRLTS). The proposed method (WRLTS) has been compared to some different estimation methods, namely the Ordinary Least Squares (OLS), Ridge Regression (RR),Robust Ridge Regression (RRR) such as Ridge LeastMedian Squares (RLMS), Ridge Least Trimmed Squares (RLTS) regression based on LTS estimator and Weighted Ridge (WRID) with respect to Standard Error. Two examples are used to illustrate the proposed method. In both examples, WRLTS is found to be the best estimator among the other methods in this paper.