Berry–Esseen-Type Estimates for Random Variables with a Sparse Dependency Graph

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-08-12 DOI:10.1007/s10959-024-01363-z

Maximilian Janisch, Thomas Lehéricy

引用次数: 0

Abstract

We obtain Berry–Esseen-type bounds for the sum of random variables with a dependency graph and uniformly bounded moments of order \(\delta \in (2,\infty ]\) using a Fourier transform approach. Our bounds improve the state-of-the-art obtained by Stein’s method in the regime where the degree of the dependency graph is large.

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具有稀疏依赖图的随机变量的贝里-埃森型估计值

我们利用傅立叶变换方法，得到了具有隶属图的随机变量之和的贝里-埃森（Berry-Esseen）型边界，以及阶为 \(\delta \in (2,\infty ]\) 的均匀约束矩。在依赖图程度很大的情况下，我们的边界改进了斯坦因方法所获得的最新水平。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.