Performance Evaluation of Some Robust Estimators in the Presence of Outliers using a Default and Adjusted Turning Constant Values

Abstract

This research work was conducted to evaluate the performance of S, M and MM robust estimators in the presence of outliers in regression model using a default and adjusted turning constant values of the Bisquare redescent weights, so as to see the impact of increasing or reducing the turning constant values on the resistibility of the robust estimators. Since it has been observed from the literature, that the previous researchers stick to the used of the default turning constant values despite the fact that the turning constant can be adjusted. A simulation study was used to compare the performance of the robust methods with five independent variables on the sample sizes 50, 150 and 300 respectively. The result of the study showed that increasing or decreasing the turning constant values for S and M estimators have a significant impact on the resistibility of the estimators on sample sizes 50, 150, and 300 respectively, while adjusting the turning constant value for MM-estimator has no impact on the robust regression result. The study also recommends that analyst should use smaller value than the default turning constant for M-estimation to have more resistibility against outlying observations in the regression models, because the smaller the turning constant value the more resistant the M-estimator. Secondly the study recommended that analyst should use a value greater than the default K value for the S-estimation, because the higher the turning constant the more resistant the S-estimator against outlying observations.