Efficiency Comparisons of Robust and Non-Robust Estimators for Seemingly Unrelated Regressions Model

Abstract

This paper studies and reviews several procedures for developing robust regression estimators of the seemingly unrelated regressions (SUR) model, when the variables are affected by outliers. To compare the robust estimators (M-estimation, S-estimation, and MM-estimation) with non-robust (traditional maximum likelihood and feasible generalized least squares) estimators of this model with outliers, the Monte Carlo simulation study has been performed. The simulation factors of our study are the number of equations in the system, the number of observations, the contemporaneous correlation among equations, the number of regression parameters, and the percentages of outliers in the dataset. The simulation results showed that, based on total mean squared error (TMSE), total mean absolute error (TMAE) and relative absolute bias (RAB) criteria, robust estimators give better performance than non-robust estimators; specifically, the MM-estimator is more efficient than other estimators. While when the dataset does not contain outliers, the results showed that the unbiased SUR estimator (feasible generalized least squares estimator) is more efficient than other estimators.