Robust estimation in the logistic regression model

This paper presents robust M-estimates based on the influence function approach for the multiple logistic regression model. Under the assumption that the sequence of distributions corresponding to the contaminated models is contiguous to the pure model, the asymptotic normality of these estimators is determined. The optimal influence function is found as the analytical solution of the minimax problem, that is by minimizing the mean-squared deviance for worst-case contamination. A numerical implementation is given with the performance of the proposed robust estimators evaluated both in a simulation study and with two real datasets.