Robust estimators for generalized linear models

• Published in: Journal of statistical planning and inference Vol. 146; pp. 31 - 48
• Main Authors: Valdora, Marina, Yohai, Víctor J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2014
• Subjects: Breakdown point; M-estimators; Transformations; Breakdown point; Transformations; M-estimators
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2013.09.016

In this paper we propose a family of robust estimators for generalized linear models. The basic idea is to use an M-estimator after applying a variance stabilizing transformation to the response. We show the consistency and asymptotic normality of these estimators. We also obtain a lower bound for their breakdown point. A Monte Carlo study shows that the proposed estimators compare favorably with respect to other robust estimators for generalized linear models with Poisson response and log link. •We introduce a class of robust estimators for generalized linear models called weighted MT-estimators.•The weighted MT-estimators are defined by means of an M-estimator after transforming the responses to stabilize their variances.•We prove the consistency and asymptotic normality of the proposed estimators.•We obtain a sharp lower bound for their breakdown point.•We report results from a Monte Carlo study showing that weighted MT-estimators compare favorably with other existing robust estimators.