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.

翻译：本文为反应和共变都极端的情况设计了一个回归型模型。 所提议方法的设计是针对反应和共变本身都是块状峰值,因而与标准的回归法相反,它考虑到一个关键事实,即限制适当标准化组成部分的分布是极端值的极值。 拟议的框架的一个重要目标是回归方块,它由一组顺从后者的退后线组成,从数据中了解拟议的模型。 为了了解拟议的模型,我们使用了伯恩斯坦多式模型,在角密度空间之前,导致在回归方块空间的诱导。 数字研究表明,拟议方法表现良好,而资金真实数据图示揭示了两个主要股票市场之间极端损失的微妙变化的有趣方面。