Comparison of the robust methods in the general linear regression model

Abstract

We compared the robust methods in the general linear regression (GLR) model through simulations. The results show that the S-type estimators produce the minimum mean squared error (MSE) of the model in all samples and the minimum standard errors of the estimators of the regression coefficients in almost all samples in all situations including the normal distribution despite their modesty in the efficiency. As an addition to the classical efficiency concept, we introduce a new efficiency concept based on the MSE of the model and the standard errors of the estimators of the regression coefficients. The simulations show that the S-type estimators are superior in terms of the efficiencies based on the MSE of the model and the standard errors of the estimators of the regression coefficients in all situations including the normal distribution. At the end of the study we give three examples one of which using a hypothetical data set and the rest being real-life data examples. The S-type estimators produce the minimum MSE value in all examples and the minimum standard error values in most of them. The simulations and examples also reveal some interesting phenomena about the regression analysis and the estimators included in this study.