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Regression-type analysis for multivariate extreme values
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Resumo(s)
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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Funding Information:
The authors thank the Editor, Associate Editor, and two Referees for their constructive remarks and fruitful recommendations. In addition, the authors thank, without implicating, Johan Segers (Université catholique de Louvain) and Raphaël Huser (King Abdullah University of Science and Technology) for insightful discussions, suggestions, and comments. M. de Carvalho acknowledges support from the Fundação para a Ciência e a Tecnologia (Portuguese NSF) through the project UID/MAT/00006/2020. A. Kumukova was supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (grant EP/L016508/01), the Scottish Funding Council, Heriot–Watt University, and the University of Edinburgh.
Publisher Copyright:
© 2022, The Author(s).
Palavras-chave
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)