A New Regression Model for Analyzing Non-Stationary Extremes in Response and Covariate Variables with an Application in Meteorology

Abstract: The paper introduces a new regression model designed for situations where both the response and covariates are non-stationary extremes. This method is specifically designed for situations where both the response variable and covariates are represented as block maxima, as the limiting distribution of suitably standardized componentwise maxima follows an extreme value copula. The framework focuses on the regression manifold, which consists of a collection of regression lines aligned with the asymptotic result. A Logistic-normal prior is applied to the space of spectral densities to gain insights into the model based on the data, resulting in an induced prior on the regression manifolds. Numerical studies demonstrate the effectiveness of the proposed method, and an analysis of real meteorological data provides intriguing insights into the relationships between extreme losses in precipitation and temperature.