Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909016197693440 |
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| author | Wu, Weichen Le, Dung Kuchibhotla, Arun Kumar Rinaldo, Alessandro |
| author_facet | Wu, Weichen Le, Dung Kuchibhotla, Arun Kumar Rinaldo, Alessandro |
| contents | We derive new Gaussian approximation for finite martingale difference sequences in $\mathbb{R}^d$ with respect to the Kolmogorov distance. Under appropriate conditions, our bounds exhibit a dependence of order $n^{-1/4}$ on the length of the sequence and of order $\mathrm{polylog}(d)$ on the dimension. As an application, we derive a high-dimensional Berry-Esseen bound over hyper-rectangles for martingale sequences generated from Markov chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03100 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance Wu, Weichen Le, Dung Kuchibhotla, Arun Kumar Rinaldo, Alessandro Probability Statistics Theory We derive new Gaussian approximation for finite martingale difference sequences in $\mathbb{R}^d$ with respect to the Kolmogorov distance. Under appropriate conditions, our bounds exhibit a dependence of order $n^{-1/4}$ on the length of the sequence and of order $\mathrm{polylog}(d)$ on the dimension. As an application, we derive a high-dimensional Berry-Esseen bound over hyper-rectangles for martingale sequences generated from Markov chains. |
| title | Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2605.03100 |