RT Journal Article
SR 00
ID 10.1214/21-AOS2087
A1 Usseglio-Carleve, Antoine
A1 Girard, Stéphane
A1 Stupfler, Gilles Claude
T1 Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models
JF The Annals of statistics
YR 2021
FD 2021-12
VO vol. 49
IS n° 6
SP 3358
OP 3382
K1 Expectiles, Extreme value analysis, Heavy-tailed distribution, Heteroscedasticity, Regression models, Residual-based estimators, Single-indes model, Tail empirical process of residuals
AB 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 has been investigated in a recent series of papers. We build here a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise; our 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 our results can be applied to a wide class of important examples, among which linear models, single-index models as well as ARMA and GARCH time series models. Our estimators are showcased on a numerical simulation study and on real sets of actuarial and financial data.
PB Institute of Mathematical Statistics
SN 2168-8966
LK https://publications.ut-capitole.fr/id/eprint/43653/
UL http://tse-fr.eu/pub/125766