The Berry-Esseen bound in de Jong's CLT

被引：0

作者：

Doebler, Christian ^{[1
]}

机构：

[1] Heinrich Heine Univ Dusseldorf, Math Nat Wissensch Fak, Dusseldorf, Germany

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 215卷

关键词：

Berry-Esseen bounds; de Jong's CLT; Degenerate U-statistics; Fourth moment theorems; Normal approximation; Exchangeable pairs; Stein's method; CENTRAL-LIMIT-THEOREM; U-STATISTICS; MOMENT;

D O I：

10.1016/j.spl.2024.110244

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove a Berry-Esseen bound in de Jong's classical CLT for normalized, completely degenerate U-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 D & ouml;bler and Peccati (2017).

引用

页数：8

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