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Berry--Esseen bounds for self-normalized sums of local dependent random variables (2104.03683v1)
Published 8 Apr 2021 in math.PR
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.