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

作　　者：Zhuo-Song Zhang 

机构地区：[1]Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen 518055,China

出　　处：《Science China Mathematics》2024年第11期2629-2652,共24页中国科学（数学英文版）

基　　金：supported by the Singapore Ministry of Education Academic Research Fund Tier 2(Grant No.MOE2018-T2-2-076)。

摘　　要：The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution.In this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment condition.Our proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other applications.Our main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.

关 键 词：Berry-Esseen bounds self-normalized sums local dependence m-dependence graph dependency 

分 类 号：O211.5[理学—概率论与数理统计]