A0471
Title: Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models
Authors: Antoine Usseglio-Carleve - Avignon Université (France) [presenting]
Gilles Stupfler - University of Angers (France)
Stephane Girard - Inria (France)
Abstract: Expectiles define a least-squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last decade. The behaviour and estimation of unconditional extreme expectiles using independent and identically distributed heavy-tailed observations have been investigated in recent papers. We build a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise; the approach is supported by general results of independent interest on residual-based extreme value estimators in heavy-tailed regression models and is intended to cope with covariates having a large but fixed dimension. We demonstrate how the results can be applied to a wide class of important examples, among which linear models, single-index models, and ARMA and GARCH time series models. The estimators are showcased on a numerical simulation study and real sets of actuarial and financial data.
