Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

This work falls within the field of statistical modeling of extreme values, a fundamental area for the analysis and prediction of rare events with potentially severe consequences in domains such as finance, engineering, and natural risk management. Its main objective is to propose a flexible method for estimating extreme conditional quantiles. Classical approaches to extreme quantile estimation suffer from several limitations, including instability in the tail of the distribution, limited flexibility in the presence of high-dimensional covariates, and the difficulty of nonparametric methods in accurately capturing asymptotic tail behavior. To address these challenges, we develop a new extreme quantile regression methodology that coherently combines extreme value theory with modern statistical learning techniques. In this presentation, we will first outline our main methodological contributions. We will then illustrate the performance of the proposed approach using both simulated and real-world data. Finally, time permitting, we will discuss the theoretical properties of the estimator, in particular its existence and consistency.