{"title":"德容的 CLT 中的 Berry-Esseen 约束","authors":"Christian Döbler","doi":"10.1016/j.spl.2024.110244","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a Berry–Esseen bound in de Jong’s classical CLT for normalized, completely degenerate <span><math><mi>U</mi></math></span>-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg–Feller type negligibility condition are sufficient for asymptotic normality. Our bound is of the same optimal order as the bound on the Wasserstein distance to normality that has recently been proved by Döbler and Peccati (2017).</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016771522400213X/pdfft?md5=8b71a50e6a7c140238a353d5821aeb07&pid=1-s2.0-S016771522400213X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"The Berry–Esseen bound in de Jong’s CLT\",\"authors\":\"Christian Döbler\",\"doi\":\"10.1016/j.spl.2024.110244\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove a Berry–Esseen bound in de Jong’s classical CLT for normalized, completely degenerate <span><math><mi>U</mi></math></span>-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg–Feller type negligibility condition are sufficient for asymptotic normality. Our bound is of the same optimal order as the bound on the Wasserstein distance to normality that has recently been proved by Döbler and Peccati (2017).</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S016771522400213X/pdfft?md5=8b71a50e6a7c140238a353d5821aeb07&pid=1-s2.0-S016771522400213X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S016771522400213X\",\"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://www.sciencedirect.com/science/article/pii/S016771522400213X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了针对归一化、完全退化的 U 统计量的 de Jong 经典 CLT 中的 Berry-Esseen 约束，即第四矩序列收敛到 3 和 Lindeberg-Feller 型可忽略性条件对渐近正态性是足够的。我们的约束与 Döbler 和 Peccati（2017）最近证明的 Wasserstein 距离正态性约束具有相同的最优阶数。
We prove a Berry–Esseen bound in de Jong’s classical CLT for normalized, completely degenerate -statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg–Feller type negligibility condition are sufficient for asymptotic normality. Our bound is of the same optimal order as the bound on the Wasserstein distance to normality that has recently been proved by Döbler and Peccati (2017).
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