Dual Induction CLT for High-dimensional m-dependent Data

06/25/2023

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by   Heejong Bong, et al.

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In this work, we provide a 1/√(n)-rate finite sample Berry-Esseen bound for m-dependent high-dimensional random vectors over the class of hyper-rectangles. This bound imposes minimal assumptions on the random vectors such as nondegenerate covariances and finite third moments. The proof uses inductive relationships between anti-concentration inequalities and Berry-Esseen bounds, which are inspired by the classical Lindeberg swapping method and the concentration inequality approach for dependent data. Performing a dual induction based on the relationships, we obtain tight Berry-Esseen bounds for dependent samples.