The Berry-Esseen Bound for High-dimensional Self-normalized Sums
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915104658817024 |
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| author | Chang, Woonyoung Takatsu, Kenta Urban, Konrad Kuchibhotla, Arun Kumar |
| author_facet | Chang, Woonyoung Takatsu, Kenta Urban, Konrad Kuchibhotla, Arun Kumar |
| contents | This manuscript studies the Gaussian approximation of the coordinate-wise maximum of self-normalized statistics in high-dimensional settings. We derive an explicit Berry-Esseen bound under weak assumptions on the absolute moments. When the third absolute moment is finite, our bound scales as $\log^{5/4}(d)/n^{1/8}$ where $n$ is the sample size and $d$ is the dimension. Hence, our bound tends to zero as long as $\log(d)=o(n^{1/10})$. Our results on self-normalized statistics represent substantial advancements, as such a bound has not been previously available in the high-dimensional central limit theorem (CLT) literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Berry-Esseen Bound for High-dimensional Self-normalized Sums Chang, Woonyoung Takatsu, Kenta Urban, Konrad Kuchibhotla, Arun Kumar Probability Statistics Theory This manuscript studies the Gaussian approximation of the coordinate-wise maximum of self-normalized statistics in high-dimensional settings. We derive an explicit Berry-Esseen bound under weak assumptions on the absolute moments. When the third absolute moment is finite, our bound scales as $\log^{5/4}(d)/n^{1/8}$ where $n$ is the sample size and $d$ is the dimension. Hence, our bound tends to zero as long as $\log(d)=o(n^{1/10})$. Our results on self-normalized statistics represent substantial advancements, as such a bound has not been previously available in the high-dimensional central limit theorem (CLT) literature. |
| title | The Berry-Esseen Bound for High-dimensional Self-normalized Sums |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2501.08979 |