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

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.

24 pages

References in corpus (3)

• Normal approximation under local dependence
• Exponential inequalities for self-normalized martingales with applications
• Normal approximation for nonlinear statistics using a concentration inequality approach