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Preprints, Working Papers, ... Year : 2023

Functional central limit theorem and Marcinkiewicz strong law of large numbers for Hilbert-valued U-statistics of absolutely regular data

Abstract

In this paper, we investigate the functional central limit theorem and the Marcinkiewicz strong law of large numbers for U-statistics having absolutely regular data and taking value in a separable Hilbert space. The novelty of our approach consists in using coupling in order to formulate a deviation inequality for original $U$-statistic, where the upper bound involves the mixing coefficient and the tail of several U-statistics of i.i.d. data. The presented results improve the known results in several directions: the case of metric space valued data is considered as well as Hilbert space valued, and the mixing rates are less restrictive in a wide range of parameters.
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Dates and versions

hal-04273319 , version 1 (07-11-2023)

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Davide Giraudo. Functional central limit theorem and Marcinkiewicz strong law of large numbers for Hilbert-valued U-statistics of absolutely regular data. 2023. ⟨hal-04273319⟩
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