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Conference papers

Kernel estimation of extreme regression risk measures

Jonathan El Methni 1 Laurent Gardes 2 Stéphane Girard 3
3 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : The Regression Conditional Tail Moment (RCTM) is the risk measure defined as the moment of order b ≥ 0 of a loss distribution above the upper α-quantile where α ∈ (0, 1) and when a covariate information is available. The purpose of this communication is first to establish the asymptotic properties of the RCTM in case of extreme losses, i.e when α → 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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Submitted on : Friday, April 6, 2018 - 3:18:59 PM
Last modification on : Friday, February 4, 2022 - 3:34:34 AM


  • HAL Id : hal-01745322, version 1


Jonathan El Methni, Laurent Gardes, Stéphane Girard. Kernel estimation of extreme regression risk measures. ICOR 2018 - 13th International Conference on Operations Research, Mar 2018, La Havane, Cuba. pp.1. ⟨hal-01745322⟩



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