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Robust estimators for generalized linear models. (English) Zbl 1279.62148
Summary: 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.

##### MSC:
 62J12 Generalized linear models (logistic models) 62F12 Asymptotic properties of parametric estimators 62F35 Robustness and adaptive procedures (parametric inference) 65C05 Monte Carlo methods
##### Keywords:
M-estimators; transformations; breakdown points
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##### References:
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