Publicação
Regression-type analysis for multivariate extreme values
| Resumo: | This paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed for the setting where the response and covariates are modeled as multivariate extreme values, and thus contrarily to standard regression methods it takes into account the key fact that the limiting distribution of suitably standardized componentwise maxima is an extreme value copula. An important target in the proposed framework is the regression manifold, which consists of a family of regression lines obeying the latter asymptotic result. To learn about the proposed model from data, we employ a Bernstein polynomial prior on the space of angular densities which leads to an induced prior on the space of regression manifolds. Numerical studies suggest a good performance of the proposed methods, and a finance real-data illustration reveals interesting aspects on the conditional risk of extreme losses in two leading international stock markets. |
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| Autores principais: | de Carvalho, Miguel |
| Outros Autores: | Kumukova, Alina; dos Reis, Gonçalo |
| Assunto: | Angular measure Bernstein polynomials Extreme value copula Joint extremes Multivariate extreme value distribution Quantile regression Statistics of extremes Statistics and Probability Engineering (miscellaneous) Economics, Econometrics and Finance (miscellaneous) |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | This paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed for the setting where the response and covariates are modeled as multivariate extreme values, and thus contrarily to standard regression methods it takes into account the key fact that the limiting distribution of suitably standardized componentwise maxima is an extreme value copula. An important target in the proposed framework is the regression manifold, which consists of a family of regression lines obeying the latter asymptotic result. To learn about the proposed model from data, we employ a Bernstein polynomial prior on the space of angular densities which leads to an induced prior on the space of regression manifolds. Numerical studies suggest a good performance of the proposed methods, and a finance real-data illustration reveals interesting aspects on the conditional risk of extreme losses in two leading international stock markets. |
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