Limit theorems for U-statistics of Bernoulli data

Abstract

In this paper, we consider U-statistics whose data is a strictly stationary sequence which can be expressed as a functional of an i.i.d. one. We establish a strong law of large numbers, a bounded law of the iterated logarithms and a central limit theorem under a dependence condition. The main ingredients for the proof are an approximation by U-statistics whose data is a functional of $\ell$ i.i.d. random variables and an analogue of the Hoeffding's decomposition for U-statistics of this type.

arXiv comment30 pages

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Cited by in corpus (1)

• U-statistics of local sample moments under weak dependence