Point process convergence for symmetric functions of high-dimensional random vectors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911775842107392 |
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| author | Heiny, Johannes Kleemann, Carolin |
| author_facet | Heiny, Johannes Kleemann, Carolin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15804 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Point process convergence for symmetric functions of high-dimensional random vectors Heiny, Johannes Kleemann, Carolin Probability Primary 60G55, Secondary 60G70, 60B12 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. |
| title | Point process convergence for symmetric functions of high-dimensional random vectors |
| topic | Probability Primary 60G55, Secondary 60G70, 60B12 |
| url | https://arxiv.org/abs/2303.15804 |