MONTE-CARLO STUDY OF SOME ROBUST ESTIMATORS THE SIMPLE LINEAR REGRESSION CASE

Abstract

In this study, Least Trimmed Squares (LTS), Theil’s Pair-wise Median (Theil) and Bayesian estimation methods (BAYES) are compared relative to the OLSE via Monte-Carlo Simulation. Variance, Bias, Mean Square Error (MSE) and Relative Mean Square Error (RMSE) are computed and used to evaluate and rank the estimators’ performance. The Simple Linear Regression model is investigated for the conditions in which the error term is assumed to be drawn from three error distributions: unit normal, lognormal and Cauchy. Theil’s non-parametric estimation procedure was found to have the strongest and most reliable performance. The second-best results are obtained from LTS method. Though it was observed that the Bayesian estimators are affected by deviation of the dataset from normality, yet it is established from the results that the Bayesian estimators performed optimally more than all other competitors, even under non normal situations (especially under the standard lognormal distribution) in some cases, except whenever the error is drawn from a heavy tail distribution (Lognormal and Cauchy). OLSE is only reliable as long as the normality assumptions hold.