Experimental and analytic comparison of the accuracy of different estimates of parameters in a linear regression model

Abstract

We consider LS-, LAD-, R-, M-, S-, LMS-, LTS-, MM-, and HBR-estimates for the parameters of a linear regression model with unknown noise distribution. With computer modeling for medium sized samples, we compare the accuracy of the considered estimates for the most popular probability distributions of noise in a regression model. For different noise distributions, we analytically compute asymptotic efficiencies of LS-, LAD-, R-, M-, S-, and LTS- estimates. We give recommendations for practical applications of these methods for different noise distributions in the model. We show examples on real datasets that support the advantages of robust estimates.