Convergence in $χ^2$ Distance to the Normal Distribution for Sums of Independent Random Variables
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912297353478144 |
|---|---|
| author | Zacharovas, Vytas |
| author_facet | Zacharovas, Vytas |
| contents | Suppose $n$ independent random variables $X_1, X_2, \dots, X_n$ have zero mean and equal variance. We prove that if the average of $χ^2$ distances between these variables and the normal distribution is bounded by a sufficiently small constant, then the $χ^2$ distance between their normalized sum and the normal distribution is $O(1/n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence in $χ^2$ Distance to the Normal Distribution for Sums of Independent Random Variables Zacharovas, Vytas Probability Suppose $n$ independent random variables $X_1, X_2, \dots, X_n$ have zero mean and equal variance. We prove that if the average of $χ^2$ distances between these variables and the normal distribution is bounded by a sufficiently small constant, then the $χ^2$ distance between their normalized sum and the normal distribution is $O(1/n)$. |
| title | Convergence in $χ^2$ Distance to the Normal Distribution for Sums of Independent Random Variables |
| topic | Probability |
| url | https://arxiv.org/abs/2503.21320 |