A Comparison of Regression Methods

Keywords: robust regression, least squares. M-estimators

Abstract: A variety of robust regression methods, as well as least squares regression, are compared. The accuracy of the estimators for the slope are assessed for the simple linear regression model, using a variety of normal and heavy-tailed error term distributions. A focus on small sample sizes allows one to determine how well guidelines based on asymptotic results hold up when the sample size is not large, and allows for the creation of alternative guidelines. Additionally, the development of an adaptive estimator is considered, and a comparison of some hypothesis testing procedures is made.