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COMPARISON OF THE ESTIMATORS OF THE LOCATION AND SCALE PARAMETERS UNDER THE MIXTURE AND OUTLIER MODELS VIA SIMULATION

Quite a few robust estimators have been proposed by many authors since the well-known estimators of location and scale, the sample mean and the sample standard deviation, are not robust to deviations from normality. There are some studies in the literature investigating the robustness of the various methods through simulation but they generally focus on investigating the performance of the estimators of location. In this study we compared the performance of two types of Huber’s M estimators (w24 and BS82), the modified maximum likelihood (MML) estimators, and the sample median and the scaled median absolute deviation (MAD) w.r.t. the sample mean and the sample standard deviation via simulation under the mixture and outlier models. Depending on the simulation results, in the estimation of location, we can suggest the general usage of the Huber’s M estimators. In the estimation of scale, the MML estimator of scale can be used unless the sample size and the extremity of contamination (k) are large. In such situations the sample standard deviation should be preferred.