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2018 Kernel estimation of extreme regression risk measures
Jonathan El Methni, Laurent Gardes, Stéphane Girard
Electron. J. Statist. 12(1): 359-398 (2018). DOI: 10.1214/18-EJS1392


The Regression Conditional Tail Moment (RCTM) is the risk measure defined as the moment of order $b\geq0$ of a loss distribution above the upper $\alpha$-quantile where $\alpha\in (0,1)$ and when a covariate information is available. The purpose of this work is first to establish the asymptotic properties of the RCTM in case of extreme losses, i.e when $\alpha\to 0$ is no longer fixed, under general extreme-value conditions on their distribution tail. In particular, no assumption is made on the sign of the associated extreme-value index. Second, the asymptotic normality of a kernel estimator of the RCTM is established, which allows to derive similar results for estimators of related risk measures such as the Regression Conditional Tail Expectation/Variance/Skewness. When the distribution tail is upper bounded, an application to frontier estimation is also proposed. The results are illustrated both on simulated data and on a real dataset in the field of nuclear reactors reliability.


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Jonathan El Methni. Laurent Gardes. Stéphane Girard. "Kernel estimation of extreme regression risk measures." Electron. J. Statist. 12 (1) 359 - 398, 2018.


Received: 1 March 2017; Published: 2018
First available in Project Euclid: 15 February 2018

zbMATH: 1388.62141
MathSciNet: MR3763910
Digital Object Identifier: 10.1214/18-EJS1392

Primary: 62G30 , 62G32
Secondary: 62E20

Keywords: asymptotic normality , Conditional tail moment , extreme-value analysis , extreme-value index , Kernel estimator , risk measures


Vol.12 • No. 1 • 2018
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