High-dimensional CLT for Sums of Non-degenerate Random Vectors: $n^{-1/2}$-rate

Abstract

In this note, we provide a Berry--Esseen bounds for rectangles in high-dimensions when the random vectors have non-singular covariance matrices. Under this assumption of non-singularity, we prove an $n^{-1/2}$ scaling for the Berry--Esseen bound for sums of mean independent random vectors with a finite third moment. The proof is essentially the method of compositions proof of multivariate Berry--Esseen bound from Senatov (2011). Similar to other existing works (Kuchibhotla et al. 2018, Fang and Koike 2020a), this note considers the applicability and effectiveness of classical CLT proof techniques for the high-dimensional case.

arXiv comment21 pages

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• Detailed proof of Nazarov's inequality
• Beyond Gaussian Approximation: Bootstrap for Maxima of Sums of Independent Random Vectors
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Cited by in corpus (1)

• Berry-Esseen Bounds for Projection Parameters and Partial Correlations with Increasing Dimension