High-dimensional Berry-Esseen Bound for $m$-Dependent Random Samples
Probability
2022-12-13 v1 Statistics Theory
Statistics Theory
Abstract
In this work, we provide a -rate finite sample Berry-Esseen bound for -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.
Cite
@article{arxiv.2212.05355,
title = {High-dimensional Berry-Esseen Bound for $m$-Dependent Random Samples},
author = {Heejong Bong and Arun Kumar Kuchibhotla and Alessandro Rinaldo},
journal= {arXiv preprint arXiv:2212.05355},
year = {2022}
}