# Regression Type Models for Extremal Dependence

## TL;DR

This paper introduces a flexible modeling framework for understanding how covariates influence the dependence structure of multivariate extreme values, with applications to temperature extremes.

## Contribution

It develops a vector generalized additive model for covariate effects on angular densities in multivariate extremes, including estimation and theoretical properties.

## Key findings

- The method accurately recovers covariate-adjusted angular densities in simulations.
- Application reveals significant dependence dynamics of extreme temperatures between resorts.
- Estimation procedure is consistent and asymptotically normal.

## Abstract

We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log-likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate-adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season. Supplementary materials for this article are available online.