A comparative study of robust estimates in regression

Classical least squares regression consisting of minimizing the sum of the squared residuals is sensitive to outliers. Many authors have proposed more robust versions of this estimator. In this paper, three classes of robust regression estimators are investigated for various real-world data using the bootstrap procedure. These are the M-estimators, the bounded influence estimators (GM-estimators) and the high breakdown point estimators. It is found that both GM-estimators and M-estimators consistently outperform the ordinary least squares method when the normality assumption is violated. High breakdown point estimators, though theoretically robust to the leverage points, cannot achieve the needed stability. Robust regression using M-estimators or GM-estimators can be a viable alternative or a supplement to ordinary least squares method.