文章基本信息

标题：Kernel estimation of extreme regression risk measures
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作者：Jonathan El Methni ; Laurent Gardes ; Stéphane Girard 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2018
卷号：12
期号：1
页码：359-398
DOI：10.1214/18-EJS1392
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.