高维随机向量对称函数的点过程收敛性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-20 DOI:10.1007/s10687-023-00482-w

Johannes Heiny, Carolin Kleemann

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引用次数: 0

摘要

证明了由 iid 高维随机向量的对称函数定义的具有依赖点的点过程序列向泊松随机量的收敛性。这也意味着固定数量的高阶统计量的联合分布收敛。作为该结果的应用，给出了简单线性秩统计量、秩型 U 统计量和样本协方差矩阵项的最大收敛到点过程收敛的概括。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Point process convergence for symmetric functions of high-dimensional random vectors

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Point process convergence for symmetric functions of high-dimensional random vectors

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint distribution of a fixed number of upper order statistics. As applications of the result a generalization of maximum convergence to point process convergence is given for simple linear rank statistics, rank-type U-statistics and the entries of sample covariance matrices.

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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.