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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.11381 |
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| _version_ | 1866929462316105728 |
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| author | Yao, Liu-Quan Liu, Song-Hao |
| author_facet | Yao, Liu-Quan Liu, Song-Hao |
| contents | In this paper, we consider the symmetric KL-divergence between the sum of independent variables and a Gaussian distribution, and obtain a convergence rates of order $O\left( \frac{\ln n}{\sqrt{n}}\right)$. The proof is based on Stein's method. The convergence rate of order $O\left( \frac{1}{\sqrt{n}}\right)$ and $O\left( \frac{1}{n}\right) $ are also obtained under higher moment condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric KL-divergence by Stein's Method Yao, Liu-Quan Liu, Song-Hao Probability 60F05, 60G50 In this paper, we consider the symmetric KL-divergence between the sum of independent variables and a Gaussian distribution, and obtain a convergence rates of order $O\left( \frac{\ln n}{\sqrt{n}}\right)$. The proof is based on Stein's method. The convergence rate of order $O\left( \frac{1}{\sqrt{n}}\right)$ and $O\left( \frac{1}{n}\right) $ are also obtained under higher moment condition. |
| title | Symmetric KL-divergence by Stein's Method |
| topic | Probability 60F05, 60G50 |
| url | https://arxiv.org/abs/2401.11381 |