High-dimensional Berry-Esseen Bound for m-Dependent Random Samples

12/10/2022

∙

by   Heejong Bong, et al.

∙

0

∙

share

In this work, we provide a (n/m)^-1/2-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 telescoping method of Chen and Shao (2004) and the recursion method of Kuchibhotla and Rinaldo (2020). Performing a dual induction based on the relationships, we obtain tight Berry-Esseen bounds for dependent samples.