Robust linear regression

Abstract

In practice, when applying a statistical method it often occurs that some observations deviate from the usual model assumptions. Least-squares (LS) estimators are very sensitive to outliers. Even one single atypical value may have a large effect on the regression parameter estimates. The goal of robust regression is to develop methods that are resistant to the possibility that one or several unknown outliers may occur anywhere in the data. In this paper, we review various robust regression methods including: M-estimate, LMS estimate, LTS estimate, S-estimate, [tau]-estimate, MM-estimate, GM-estimate, and REWLS estimate. Finally, we compare these robust estimates based on their robustness and efficiency through a simulation study. A real data set application is also provided to compare the robust estimates with traditional least squares estimator.