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

被引：0

作者：

Heiny, Johannes ^{[1
]}

Kleemann, Carolin ^{[2
]}

机构：

[1] Stockholm Univ, Dept Math, Albano Hus 1, S-10691 Stockholm, Sweden

[2] Ruhr Univ Bochum, Fak Math, Univ Str 150, D-44780 Bochum, Germany

来源：

EXTREMES | 2024年 / 27卷 / 02期

关键词：

Point process convergence; Extreme value theory; Poisson process; Gumbel distribution; High-dimensional data; U-statistics; Kendall's tau; Spearman's rho; POISSON APPROXIMATION; INDEPENDENCE; DEVIATIONS; STATISTICS;

D O I：

10.1007/s10687-023-00482-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：185 / 217

页数：33

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