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Deviation and moment inequalities for Banach-valued $U$-statistics (2405.01902v1)
Published 3 May 2024 in math.PR, math.ST, and stat.TH
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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