Inférence statistique dans les modèles de régression non paramétriques

Abstract

We have choosen to investigate the statistic inference in nonpara- metric regression models by studying kernel densities and regres- sion estimators under different assumptions . This work is organised in two parts : The asymptotic properties of density and regression estimators are studied first under independence assumption, particulary, conver- gence, normality and the choice of the smoothing window. In the second part, we go the generalized notion of weak depen- dence established by Doukhan and Louhichi (1999) to extend conver- gence and normality properties. This allows to deal with time se- ries, we show after, our result on a recursive kernel estimator under weak dependence, convergence in mean square error, and normality are obtained. Simulation study is done on weak dependent models.