Tail Bounds for Canonical $U$-Statistics and $U$-Processes with Unbounded Kernels
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917991739817984 |
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| author | Chakrabortty, Abhishek Kuchibhotla, Arun K. |
| author_facet | Chakrabortty, Abhishek Kuchibhotla, Arun K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tail Bounds for Canonical $U$-Statistics and $U$-Processes with Unbounded Kernels Chakrabortty, Abhishek Kuchibhotla, Arun K. Statistics Theory Probability 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. |
| title | Tail Bounds for Canonical $U$-Statistics and $U$-Processes with Unbounded Kernels |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2504.01318 |