Characterizing extremal dependence on a hyperplane
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918159796142080 |
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| author | Wan, Phyllis |
| author_facet | Wan, Phyllis |
| contents | In this paper, we characterize the extremal dependence of $d$ asymptotically dependent variables by a class of random vectors on the $(d-1)$-dimensional hyperplane perpendicular to the diagonal vector $\mathbf1=(1,\ldots,1)$. This translates analyses of multivariate extremes to that on a linear vector space, opening up possibilities for applying existing statistical techniques that are based on linear operations. As an example, we demonstrate obtaining lower-dimensional approximations of the tail dependence through principal component analysis. Additionally, we show that the widely used Hüsler-Reiss family is characterized by a Gaussian family residing on the hyperplane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing extremal dependence on a hyperplane Wan, Phyllis Statistics Theory 62G32, 62H05 In this paper, we characterize the extremal dependence of $d$ asymptotically dependent variables by a class of random vectors on the $(d-1)$-dimensional hyperplane perpendicular to the diagonal vector $\mathbf1=(1,\ldots,1)$. This translates analyses of multivariate extremes to that on a linear vector space, opening up possibilities for applying existing statistical techniques that are based on linear operations. As an example, we demonstrate obtaining lower-dimensional approximations of the tail dependence through principal component analysis. Additionally, we show that the widely used Hüsler-Reiss family is characterized by a Gaussian family residing on the hyperplane. |
| title | Characterizing extremal dependence on a hyperplane |
| topic | Statistics Theory 62G32, 62H05 |
| url | https://arxiv.org/abs/2411.00573 |