Strong Gaussian Approximation for the Sum of Random Vectors

2021/06/10 by Nazar Buzun, Buzun, Nazar, Nikolay Shvetsov +3
Mathematics · #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2106.05890

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 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).

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

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