Central Limit Theorem for Rényi Divergence of Infinite Order
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914840585437184 |
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| author | Bobkov, Sergey G. Götze, Friedrich |
| author_facet | Bobkov, Sergey G. Götze, Friedrich |
| contents | For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities $p_n$ of $Z_n$, this is a strengthened variant of the local limit theorem taking the form $\sup_x (p_n(x) - φ(x))/φ(x) \rightarrow 0$ as $n \rightarrow \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Central Limit Theorem for Rényi Divergence of Infinite Order Bobkov, Sergey G. Götze, Friedrich Probability 60E, 60F For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities $p_n$ of $Z_n$, this is a strengthened variant of the local limit theorem taking the form $\sup_x (p_n(x) - φ(x))/φ(x) \rightarrow 0$ as $n \rightarrow \infty$. |
| title | Central Limit Theorem for Rényi Divergence of Infinite Order |
| topic | Probability 60E, 60F |
| url | https://arxiv.org/abs/2402.02259 |