An exponential inequality for Hilbert-valued U-statistics of i.i.d. data
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912033585233920 |
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| author | Giraudo, Davide |
| author_facet | Giraudo, Davide |
| contents | 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 are 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, weighted U-statistics and incomplete U-statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An exponential inequality for Hilbert-valued U-statistics of i.i.d. data Giraudo, Davide Probability Statistics Theory 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 are 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, weighted U-statistics and incomplete U-statistics. |
| title | An exponential inequality for Hilbert-valued U-statistics of i.i.d. data |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2409.11737 |