U-statistiques conditionnelles universellement consistantes pour des modèles de Markov cachés

Abstract

A general class of conditional U-statistics was introduced by W. Stute [3] as a generalization of the Nadaraya–Watson estimates of a regression function. It was shown that such statistics are universally consistent (Stute [3]). Also, universal consistency of the window and k_n-nearest neighbor estimators (as two special cases of the conditional U-statistics) were proved by Stute [3]. In this paper, we extend these results from the independent case to dependent case.