Model selection in logistic regression

This paper is devoted to model selection in logistic regression. We extend the model selection principle introduced by Birg\é and Massart (2001) to logistic regression model. This selection is done by using penalized maximum likelihood criteria. We propose in this context a completely data-driven criteria based on the slope heuristics. We prove non asymptotic oracle inequalities for selected estimators. Theoretical results are illustrated through simulation studies.