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

Davide Giraudo

Journal of Multivariate Analysis, 2025, vol. 207, issue C

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 is 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, incomplete U-statistics and weighted U-statistics.

Keywords: U-statistics; Martingales; Hilbert space (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2025.105406

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