Electronic Journal of Statistics

Kernel estimation of extreme regression risk measures

Jonathan El Methni, Laurent Gardes, and Stéphane Girard

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 12, Number 1 (2018), 359-398.

Dates
Received: March 2017
First available in Project Euclid: 15 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1518663657

Digital Object Identifier
doi:10.1214/18-EJS1392

Mathematical Reviews number (MathSciNet)
MR3763910

Zentralblatt MATH identifier
1388.62141

Subjects
Primary: 62G32: Statistics of extreme values; tail inference 62G30: Order statistics; empirical distribution functions
Secondary: 62E20: Asymptotic distribution theory

Keywords
Conditional tail moment kernel estimator asymptotic normality risk measures extreme-value index extreme-value analysis

Rights
Creative Commons Attribution 4.0 International License.

Citation

El Methni, Jonathan; Gardes, Laurent; Girard, Stéphane. Kernel estimation of extreme regression risk measures. Electron. J. Statist. 12 (2018), no. 1, 359--398. doi:10.1214/18-EJS1392. https://projecteuclid.org/euclid.ejs/1518663657


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