Estimation non-paramétrique de la fonction de régression

Abstract

"The purpose of this dissertation is to establish asymptotic results of a kernel type estimator of the regression function. This estimator is analogous to the Nadaraya-Watson estimator but the response variable is subject to twice censorship. We are conserned with the pointwise and uniform convergence rate and asymptotic normality. The used convergence mode is the almost complete convergence’s. This notion of almost complete convergence leads to almost sure convergence. We also develop the article of Messaci(2010) who introduced this estimator and the one of Messaci and Nemouchi(2011) which proves a law of the iterated logarithm of the estimator of Patilea et Rolin(2006) of the survival function. Let us note that this estimator is explicitly involved in the expression of the kernel estimator of the regression that is the subject of our study. We will also give illustrations of our results on simulated data. Our framework is that of nonparametric estimation of regression and censored data"