Berry--Esseen bounds for self-normalized sums of local dependent random variables

TL;DR

This paper establishes optimal Berry--Esseen bounds for self-normalized sums of locally dependent random variables, using Stein's method and concentration inequalities, with applications to m-dependent variables and graph dependencies.

Contribution

It provides the first optimal Berry--Esseen bounds for self-normalized sums under local dependence conditions, extending classical results to dependent data.

Findings

Optimal Berry--Esseen bounds achieved for local dependent variables

Bounds apply to m-dependent and graph-dependent random variables

Method utilizes Stein's method and randomized concentration inequalities

Abstract

In this paper, we prove a Berry--Esseen bound with optimal order for self-normalized sums of local dependent random variables under some mild dependence conditions. The proof is based on Stein's method and a randomized concentration inequality. As applications, we obtain optimal Berry--Esseen bounds for $m$-dependent random variables and graph dependency.