用Stein方法分析高维数据中独立检验的非均匀界

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-02-03 DOI:10.1155/2019/8641870

N. Rerkruthairat

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引用次数: 1

摘要

Stein方法给出了基于样本相关系数平方和的随机变量的Berry-Essen界，该界用于检验高维中的完全独立性。尽管Berry-Esseen界可以应用于R中的所有实数，但如果z是固定的，则实数z处的非均匀界通常提供更尖锐的界。本文用Stein方法给出了最优速率为1/0.5+|z|·O1/m的随机变量在正态近似上的非均匀界的第一个版本。

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A Nonuniform Bound to an Independent Test in High Dimensional Data Analysis via Stein’s Method

The Berry-Esseen bound for the random variable based on the sum of squared sample correlation coefficients and used to test the complete independence in high diemensions is shown by Stein’s method. Although the Berry-Esseen bound can be applied to all real numbers in R, a nonuniform bound at a real number z usually provides a sharper bound if z is fixed. In this paper, we present the first version of a nonuniform bound on a normal approximation for this random variable with an optimal rate of 1/0.5+|z|·O1/m by using Stein’s method.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.