An exponential inequality for Hilbert-valued U-statistics of i.i.d. data

2024/09/18 by Giraudo, Davide
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2409.11737

Abstract

In this paper, we establish an exponential inequality for U-statistics of i.i.d. data, varying kernel and taking values in a separable Hilbert space. The bound are expressed as a sum of an exponential term plus an other one involving the tail of a sum of squared norms. We start by the degenerate case. Then we provide applications to U-statistics of not necessarily degenerate fixed kernel, weighted U-statistics and incomplete U-statistics.

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