{"title":"Berry–Esseen-Type Estimates for Random Variables with a Sparse Dependency Graph","authors":"Maximilian Janisch, Thomas Lehéricy","doi":"10.1007/s10959-024-01363-z","DOIUrl":null,"url":null,"abstract":"<p>We obtain Berry–Esseen-type bounds for the sum of random variables with a dependency graph and uniformly bounded moments of order <span>\\(\\delta \\in (2,\\infty ]\\)</span> 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.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"53 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Theoretical Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10959-024-01363-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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.
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.
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