Graphical models for multivariate extremes
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911770766999552 |
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| author | Engelke, Sebastian Hentschel, Manuel Lalancette, Michaël Röttger, Frank |
| author_facet | Engelke, Sebastian Hentschel, Manuel Lalancette, Michaël Röttger, Frank |
| contents | Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in high-dimensional problems. In this work, we provide the fundamental concepts of extremal graphical models and discuss recent advances in the field. Different existing perspectives on graphical extremes are presented in a unified way through graphical models for exponent measures. We discuss the important cases of nonparametric extremal graphical models on simple graph structures, and the parametric class of Hüsler--Reiss models on arbitrary undirected graphs. In both cases, we describe model properties, methods for statistical inference on known graph structures, and structure learning algorithms when the graph is unknown. We illustrate different methods in an application to flight delay data at US airports. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphical models for multivariate extremes Engelke, Sebastian Hentschel, Manuel Lalancette, Michaël Röttger, Frank Methodology Statistics Theory 62G32 (Primary) 62H22 (Secondary) Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in high-dimensional problems. In this work, we provide the fundamental concepts of extremal graphical models and discuss recent advances in the field. Different existing perspectives on graphical extremes are presented in a unified way through graphical models for exponent measures. We discuss the important cases of nonparametric extremal graphical models on simple graph structures, and the parametric class of Hüsler--Reiss models on arbitrary undirected graphs. In both cases, we describe model properties, methods for statistical inference on known graph structures, and structure learning algorithms when the graph is unknown. We illustrate different methods in an application to flight delay data at US airports. |
| title | Graphical models for multivariate extremes |
| topic | Methodology Statistics Theory 62G32 (Primary) 62H22 (Secondary) |
| url | https://arxiv.org/abs/2402.02187 |