{"title":"具有稀疏依赖图的随机变量的贝里-埃森型估计值","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10959-024-01363-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10959-024-01363-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Berry–Esseen-Type Estimates for Random Variables with a Sparse Dependency Graph
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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