Limit Distribution for Conditional U-Statistics for Dependent Processes

Abstract

This paper deals with the studies of asymptotic normality and strong consistency of conditional U-statistics for dependent processes (including conditional mixing) under some regularity conditions. The novelty of the paper is that it unifies non parametric regression theory of stochastic processes (Bosq {1996)) with the theory of conditional U-statistics introduced by Stute (1991, 1994) and Liero (1991).

Keywords

Conditional U-statistics Nonparametric regression Prediction and forecasting Consistency and asymptotic normality.