  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 both the response and covariates are themselves block maxima, 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 comovements
of extreme losses between two leading stock markets.
