A0253
Title: A general theory for extremal regression in heavy-tailed models
Authors: Abdelaati Daouia - Toulouse School of Economics (France) [presenting]
Yasser Abbas - Fondation Jean-Jacques Laffont (France)
Gilles Stupfler - University of Angers (France)
Abstract: Studying rare events at the heavy tails of conditional Pareto-type distributions, in the presence of high-dimensional covariates, is a burgeoning science with many applications in actuarial, financial, and environmental risk management. The most prominent risk measures to quantify these events utilize conditional quantiles, expected shortfall, and expectiles at extreme levels. The few attempts to tackle this extreme value problem involve location-scale regression models with heavy-tailed noise. A more flexible and complex model is employed that better balances model generality with estimation efficiency. A general theory is developed that relies on residual-based estimators of the three regression risk measures at both intermediate and extreme levels, and their asymptotic behavior is fully explored in generic settings. Simple sufficient criteria are also provided for verifying the main high-level assumption, which facilitates the construction of weighted Gaussian approximations for the tail quantile residual process, ultimately ensuring the asymptotic normality of all produced extreme value estimators. This generic extremal regression framework is then applied to linear, nonlinear, and nonparametric estimation scenarios. Simulations show the undeniable potential of the methodology for various distribution types, outperforming the best available competing estimation approaches. An application to real financial data further solidifies their dominance.
