Multivariate extreme value theory
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912169262579712 |
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| author | Naveau, Philippe Segers, Johan |
| author_facet | Naveau, Philippe Segers, Johan |
| contents | When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate excesses over high thresholds as modelled by the family of multivariate generalized Pareto distributions. The formulation in terms of failure sets in the sample space intersecting the sample cloud leads to the over-arching perspective of point processes. Max-stable or generalized extreme value distributions are finally obtained as limits of vectors of componentwise maxima by considering the event that a certain region of the sample space does not contain any observation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18477 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multivariate extreme value theory Naveau, Philippe Segers, Johan Statistics Theory 62G32 When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate excesses over high thresholds as modelled by the family of multivariate generalized Pareto distributions. The formulation in terms of failure sets in the sample space intersecting the sample cloud leads to the over-arching perspective of point processes. Max-stable or generalized extreme value distributions are finally obtained as limits of vectors of componentwise maxima by considering the event that a certain region of the sample space does not contain any observation. |
| title | Multivariate extreme value theory |
| topic | Statistics Theory 62G32 |
| url | https://arxiv.org/abs/2412.18477 |