Strong Gaussian Approximation for the Sum of Random Vectors
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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 by distribution for the maximum norm in a high-dimensional setting (p >n).
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