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A Comprehensive Evaluation of M-estimators for Linear Regression Model

V. Yildirim, K. M. Kantar

Abstract


It is well-known that ordinary least squares estimator for estimating regression parameters is very sensitive to outliers, and thus, can lead to very misleading results. To cope with this problem, the robust estimators have been developed. One of the well-known robust estimators is M-estimators. In the literature, numerous M-estimators have been proposed. In this paper, an attempt is made to review and evaluate M-estimators. For this reason, a comprehensive simulation study is carried out to evaluate the M-estimators in terms of (i) the effect of choice of initial parameters (ii) root mean square error at various non-normal error distributions. In the result of the study, we give some recommendations on which M-estimator is superior to others under what conditions.

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