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Title: Regression-type analysis for multivariate extreme values Authors:  Miguel de Carvalho - FCiencias.ID - Associacao para a Investigacao e Desenvolvimento de Ciencias (Portugal) [presenting]
Alina Kumukova - University of Edinburgh (United Kingdom)
Goncalo dos Reis - University of Edinburgh (United Kingdom)
Abstract: A regression-type model is presented 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 contrary 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 of the conditional risk of extreme losses in two leading international stock markets.