Usseglio-Carleve, Antoine, Girard, Stéphane and Stupfler, Gilles Claude (2021) Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models. The Annals of statistics, vol. 49 (n° 6). pp. 3358-3382.

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Identification Number : 10.1214/21-AOS2087


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.

Item Type: Article
Language: English
Date: December 2021
Refereed: Yes
Place of Publication: Etats-Unis
Uncontrolled Keywords: Expectiles, Extreme value analysis, Heavy-tailed distribution, Heteroscedasticity, Regression models, Residual-based estimators, Single-indes model, Tail empirical process of residuals
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 28 Jul 2021 22:31
Last Modified: 11 Mar 2022 16:32
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