Limit theorems for U-statistics of Bernoulli data

04/15/2019

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by   Davide Giraudo, et al.

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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 ℓ i.i.d. random variables and an analogue of the Hoeffding's decomposition for U-statistics of this type.