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Robust estimation in the logistic regression model. (English) Zbl 0839.62030
Rieder, Helmut (ed.), Robust statistics, data analysis, and computer intensive methods. In honor of Peter Huber’s 60th birthday. New York, NY: Springer-Verlag. Lect. Notes Stat., Springer-Verlag. 109, 17-34 (1996).
Summary: A new class of robust and Fisher-consistent \(M\)-estimates for the logistic regression models is introduced. We show that these estimates are consistent and asymptotically normal. Their robustness is studied through the computation of asymptotic bias curves under point-mass contamination for the case when the covariates follow a multivariate normal distribution. We illustrate the behavior of these estimates with two data sets. Finally, we mention some possible extensions of these \(M\)-estimates for a multinomial response.
For the entire collection see [Zbl 0832.00020].

62F35 Robustness and adaptive procedures (parametric inference)
62J12 Generalized linear models (logistic models)
62F12 Asymptotic properties of parametric estimators