Deviation and moment inequalities for Banach-valued $U$-statistics

Davide Giraudo

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arXiv · 2405.01902

Deviation and moment inequalities for Banach-valued $U$-statistics

Davide Giraudo

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Abstract

We show a deviation inequality for U-statistics of independent data taking values in a separable Banach space which satisfies some smoothness assumptions. We then provide applications to rates in the law of large numbers for U-statistics, a H{\"o}lderian functional central limit theorem and a moment inequality for incomplete $U$-statistics.

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BibTeX RIS

Davide Giraudo. 2024-05-03. Deviation and moment inequalities for Banach-valued $U$-statistics. https://arxiv.org/abs/2405.01902

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