A comparison of five robust regression methods with ordinary least squares: relative efficiency, bias and test of the null hypothesis

A Monte Carlo simulation was used to generate data for a comparison of five 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 MM estimation, are commercially available. Three authormodified variations on MM were also included (MM1, MM2, and MM3). Design parameters that were varied include sample size (n=60 and n=180), number of independent predictor variables (2, 3 and 6), outlier density (0%, 5% and 15%) and outlier location (2x,2y s, 8x8y s, 4x,8y s and 8x,4y s). Criteria on which the regression methods were measured 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.