Abstract
Monte Carlo simulations were used to generate data for a comparison of 5 robust regression estimation methods with ordinary least squares (OLS) under 36 different outlier data configurations. Two of the robust estimators, least absolute value (LAV) estimation and minimum m-estimation (MM), are available in certain statistical software packages. Three author-written variations of MM were included (MM1, MM2, and MM3). Design parameters that were varied included sample size, number of independent predictor variables, outlier density, and outlier location. Criteria on which the regression methods were compared are relative efficiency, bias, and a test of the null hypothesis. Results indicated that MM2 was the best performing robust estimator on relative efficiency. The best performing estimator on bias was MM1. The best performing regression method on the test of the null hypothesis was MM2. Overall, the MM-type robust regression methods outperformed OLS and LAV on relative efficiency, bias, and the test of the null hypothesis.
