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

TL;DR

This paper proposes a novel regression model for analyzing non-stationary extreme responses and covariates, especially in meteorology, using extreme value copulas and Bayesian priors, with demonstrated effectiveness on real data.

Contribution

It introduces a new regression framework for non-stationary extremes using extreme value copulas and Bayesian spectral density priors, advancing analysis of complex meteorological data.

Findings

Effective modeling of non-stationary extremes in response and covariates.

Insights into relationships between extreme precipitation and temperature.

Validated through numerical studies and real meteorological data analysis.

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.