德容的 CLT 中的 Berry-Esseen 约束

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-08-13 DOI:10.1016/j.spl.2024.110244

Christian Döbler

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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。

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The Berry–Esseen bound in de Jong’s CLT

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 Döbler and Peccati (2017).

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.