Robust Regression M-Estimation, S-Estimation, and MM-Estimation in Multiple Regression

Abstract

In classical multiple regression, the ordinary least squares estimation is the best method if assumptions are met to obtain regression weights when analyzing data. However, if the data does not satisfy some of these assumptions, then sample estimates and results can be misleading. Therefore, statistical techniques that are able to cope with or to detect outlying observations have been developed. Robust regression is an important method for analyzing data that are contaminated with outliers. It can be used to detect outliers and to provide resistant results in the presence of outliers. The purpose of this study is compare robust regression M-estimation, S-estimation, and MM-estimation with ordinary least square methods via simulation study. The simulation study is used in determine which methods best in all of the linear regression scenarios.