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

2020/09/28 by Arun Kumar Kuchibhotla, Alessandro Rinaldo, Kuchibhotla, Arun Kumar +1 · 1 citation
Mathematics · #Random Matrices and Applications #Advanced Algebra and Geometry #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2009.13673

Abstract

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

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• High-dimensional normal approximations for sums of Langevin Markov chains
• Berry-Esseen Bounds for Projection Parameters and Partial Correlations\n with Increasing Dimension

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