Asymptotic Normality of $U$-Statistics is Equivalent to Convergence in the Wasserstein Distance
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917662763778048 |
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| author | Kroll, Marius |
| author_facet | Kroll, Marius |
| contents | We prove the claim in the title under mild conditions which are usually satisfied when trying to establish asymptotic normality. We assume strictly stationary and absolutely regular data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06477 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Normality of $U$-Statistics is Equivalent to Convergence in the Wasserstein Distance Kroll, Marius Statistics Theory Primary: 60F05, 60F25. Secondary: 60G50 We prove the claim in the title under mild conditions which are usually satisfied when trying to establish asymptotic normality. We assume strictly stationary and absolutely regular data. |
| title | Asymptotic Normality of $U$-Statistics is Equivalent to Convergence in the Wasserstein Distance |
| topic | Statistics Theory Primary: 60F05, 60F25. Secondary: 60G50 |
| url | https://arxiv.org/abs/2405.06477 |