Robust estimators for generalized linear models

• 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.

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.