Tail Bounds for Canonical $U$-Statistics and $U$-Processes with Unbounded Kernels

Abhishek Chakrabortty; Arun K. Kuchibhotla

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arXiv · 2504.01318

Tail Bounds for Canonical $U$-Statistics and $U$-Processes with Unbounded Kernels

Abhishek Chakrabortty·Arun K. Kuchibhotla

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Abstract

In this paper, we prove exponential tail bounds for canonical (or degenerate) $U$-statistics and $U$-processes under exponential-type tail assumptions on the kernels. Most of the existing results in the relevant literature often assume bounded kernels or obtain sub-optimal tail behavior under unbounded kernels. We obtain sharp rates and optimal tail behavior under sub-Weibull kernel functions. Some examples from nonparametric and semiparametric statistics literature are considered.

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Abhishek Chakrabortty, Arun K. Kuchibhotla. 2025-04-02. Tail Bounds for Canonical $U$-Statistics and $U$-Processes with Unbounded Kernels. https://arxiv.org/abs/2504.01318

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