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Limit Distribution for Conditional U-Statistics for Dependent Processes

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).