A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n)
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913367264854016 |
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| author | Ayvazyan, Sagak A. Ulyanov, Vladimir V. |
| author_facet | Ayvazyan, Sagak A. Ulyanov, Vladimir V. |
| contents | The "typical" asymptotic behavior of the weighted sums of independent random vectors in $k$-dimensional space is considered. It is shown that in this case the rate of convergence in the multivariate central limit theorem is of order $O(1/n)$. This extends the one-dimensional Klartag and Sodin (2011) result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_05815 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n) Ayvazyan, Sagak A. Ulyanov, Vladimir V. Probability 60F05 (Primary) The "typical" asymptotic behavior of the weighted sums of independent random vectors in $k$-dimensional space is considered. It is shown that in this case the rate of convergence in the multivariate central limit theorem is of order $O(1/n)$. This extends the one-dimensional Klartag and Sodin (2011) result. |
| title | A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n) |
| topic | Probability 60F05 (Primary) |
| url | https://arxiv.org/abs/2112.05815 |