Modelling joint extreme events via boosting distributional copula regression

Annika Strömer, University of Marburg

Co-authors: Miguel de Carvalho, University of Edinburgh; Nadja Klein, Karlsruhe Institute of Technology; Francisco Gude, Health Research Institute of Santiago de Compostela (IDIS); Andreas Mayr, University of Marburg

Abstract: Extreme events are a major challenge for traditional statistical models, which are limited in their ability to model rare multivariate occurrences characterized by simultaneous extremes in several dimensions. Even advanced methods such as copula regression do not adequately capture the tails of the distribution where rare events occur. Extreme value copulas provide a versatile solution by combining multivariate extreme value theory and copulas to model complex dependencies between extreme events. In this work, we propose an approach that combines model-based boosting with distributional copula regression to address these challenges. Our method simultaneously estimates all distribution parameters, including the copula parameter, as functions of potentially different covariates, while incorporating data-driven variable selection. Through a Galician cohort study as well as simulations, we illustrate the flexibility of our approach, also in high-dimensional settings where classical estimation frameworks reach their limits.