Open Access Open Access  Restricted Access Subscription or Fee Access

A Comprehensive Evaluation of M-estimators for Linear Regression Model

V. Yildirim, K. M. Kantar


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.


Linear regression model, non-normal error terms, M-estimators, Monte Carlo simulation, breakdown plot, outliers.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.