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

2021/04/08 by Zhuo-Song Zhang, Zhang, Zhuo-Song
Decision Sciences · Mathematics · #FOS: Mathematics #Limits and Structures in Graph Theory #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2104.03683

openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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