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arXiv · 2106.05890

Strong Gaussian Approximation for the Sum of Random Vectors

Nazar Buzun·Nikolay Shvetsov·Dmitry V. Dylov
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Abstract

This paper derives a new strong Gaussian approximation bound for the sum of independent random vectors. The approach relies on the optimal transport theory and yields \textit{explicit} dependence on the dimension size $p$ and the sample size $n$. This dependence establishes a new fundamental limit for all practical applications of statistical learning theory. Particularly, based on this bound, we prove approximation in distribution for the maximum norm in a high-dimensional setting ($p >n$).

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Nazar Buzun, Nikolay Shvetsov, Dmitry V. Dylov. 2021-06-10. Strong Gaussian Approximation for the Sum of Random Vectors. https://arxiv.org/abs/2106.05890

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