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

IF 1.1 3区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Extremes Pub Date : 2023-12-20 DOI:10.1007/s10687-023-00482-w

Johannes Heiny, Carolin Kleemann

引用次数: 0

Abstract

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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高维随机向量对称函数的点过程收敛性

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。

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来源期刊

Extremes MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY

CiteScore

2.20

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Extremes publishes original research on all aspects of statistical extreme value theory and its applications in science, engineering, economics and other fields. Authoritative and timely reviews of theoretical advances and of extreme value methods and problems in important applied areas, including detailed case studies, are welcome and will be a regular feature. All papers are refereed. Publication will be swift: in particular electronic submission and correspondence is encouraged. Statistical extreme value methods encompass a very wide range of problems: Extreme waves, rainfall, and floods are of basic importance in oceanography and hydrology, as are high windspeeds and extreme temperatures in meteorology and catastrophic claims in insurance. The waveforms and extremes of random loads determine lifelengths in structural safety, corrosion and metal fatigue.