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arXiv · 2303.15804

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

Johannes Heiny·Carolin Kleemann
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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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Johannes Heiny, Carolin Kleemann. 2023-03-28. Point process convergence for symmetric functions of high-dimensional random vectors. https://arxiv.org/abs/2303.15804

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