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

Autor:	Heiny, Johannes, Kleemann, Carolin
Rok vydání:	2023
Předmět:	Mathematics - Probability Primary 60G55 Secondary 60G70 60B12
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.15804 Zobrazit plný text záznamu View this record from Arxiv