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<p>We show a deviation inequality for <i>U</i>-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 <i>U</i>-statistics, a Hölderian functional central limit theorem and a moment inequality for incomplete <i>U</i>-statistics.</p>

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Deviation and Moment Inequalities for Banach-Valued U-statistics

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Davide Giraudo

摘要

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 Hölderian functional central limit theorem and a moment inequality for incomplete U-statistics.