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

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

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 cas...

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Bibliographic Details
Main Author: Giraudo, Davide
Format: Journal Article
Language:English
Published: 18-09-2024
Subjects:
Mathematics - Probability
Mathematics - Statistics Theory
Statistics - Theory
Online Access:Get full text
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Summary: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.
DOI:10.48550/arxiv.2409.11737