Orateur
Description
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. In this work, we employ a more flexible and complex model which better balances model generality with estimation efficiency. We develop a general theory that relies on residual-based estimators of the three regression risk measures at both intermediate and extreme levels, and fully explore their asymptotic behavior in generic settings. We also provide simple sufficient criteria for verifying our 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. We then apply this generic extremal regression framework to linear, nonlinear and nonparametric estimation scenarios. Simulations show the undeniable potential of our methodology for various distribution types, outperforming the best available competing estimation approaches. An application to real financial data further solidifies their dominance.