A COMPARATIVE STUDY OF SOME ROBUST ESTIMATORS
Keywords:
Outlier(s), Robust Estimator, OLS, Robust M, Robust MM, Robust S, Robust LTS, Robust LMS, Robust LAD, MSE.Abstract
In the presence of outliers, Ordinary Least Square estimator is found to be inefficient. In this paper, some robust estimators and OLS were used to estimate the parameters of linear regression model in the presents and absents of outlier(s). Linear regression models with three and seven predictors (p = 3 and p = 7) each at four levels of percentage of outliers (????1% = 0%, 5%, 10% ???????????? 20%), three levels of variance of outliers (???????????????????????????????????? 2 = 50, 100 ???????????? 250) and five levels of sample size (???? = 20, 30, 40, 60 ???????????? 100) were considered through Monte Carlo experiments. The experiments were carried out 2000 times, and the performances of these Robust estimators and Ordinary Least Square were investigated and compared using the Mean Square Error (MSE) criterion. Results show that when there is no outlier in the data, at all situations, Ordinary Least Squares (OLS) is the most efficient estimator among the estimators considered. But when outlier(s) exists in the data, Robust MM consistently performed more efficiently than all other methods of parameter estimation of linear regression model considered. It also shows that efficiency of these estimators increased as the sample size increased. Also, variance of outliers and percentage of outliers affect the efficiency of these estimators.
