Using Standard Error to Find the Best Robust Regression in Presence of Multicollinearity and Outliers

Abstract

Multicollinearity and outliers are seen as one of the most common problems in the models of multiple linear regression. In the present paper, a robust ridge regression is proposed on the basis of weighted ridge least trimmed squares (WRLTS). The suggested method WRLTS is compared with the following methods of estimation: The Ordinary Least Squares (OLS), Ridge Regression (RR), Robust Ridge Regression (RRR), such as Ridge Least Median Squares (RLMS), Ridge Least Trimmed Squares (RLTS), regression which is based on LTS estimator and Weighted Ridge (WRID) as far as Standard Error is concerned. For the sake of illustration of the suggested method, two examples are given through the use of R programming to test the data. Both examples have shown that WRLTS is the best estimator in comparison to the other methods in the present paper.