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

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  • Giraudo, Davide

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.

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  • Giraudo, Davide, 2025. "An exponential inequality for Hilbert-valued U-statistics of i.i.d. data," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:jmvana:v:207:y:2025:i:c:s0047259x25000016
    DOI: 10.1016/j.jmva.2025.105406
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    References listed on IDEAS

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