Etude de modèles semi et non paramétriques pour des données censurées.

Abstract

In this dissertation, we are interested in kernel estimation of the density and the failure rate for c ensored data. There exist seve ral kinds of censorship and we fo cus on right, doubly and twi ce censored data mo de ls. We consider a general framework of censorship, including all these mo dels, and we prove a result on the asymptotic normality of a kernel de nsi ty estimator that we intro duce. This result allows us to deduce the asymptotic normality of the density and failure rate e sti mates for the ab ove-mentioned censorship mo dels. We also establish the mean square convergence, with rates, of the same estimators in the case of twice censored data. In a second part of the dissertation, we study semiparametric mo dels which verify linear constraints involving an unknown parameter. We assume that the variable of interest is right c ensored and we use the theory of divergences to construct estimates for the pa ram eter of interest. Simulation studies are presented in order to illustrate the p erformances of the di erent studied estim ators.