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Nonparametric extreme conditional expectile estimation

Stéphane Girard 1 Gilles Stupfler 2 Antoine Usseglio-Carleve 1
1 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 : Expectiles and quantiles can both be defined as the solution of minimization problems. Contrary to quantiles though, expectiles are determined by tail expectations rather than tail probabilities, and define a coherent risk measure. For these two reasons in particular, expectiles have recently started to be considered as serious candidates to become standard tools in actuarial and financial risk management. However, expectiles and their sample versions do not benefit from a simple explicit form, making their analysis significantly harder than that of quantiles and order statistics. This difficulty is compounded when one wishes to integrate auxiliary information about the phenomenon of interest through a finite-dimensional covariate, in which case the problem becomes the estimation of conditional expectiles. In this paper, we exploit the fact that the expectiles of a distribution F are in fact the quantiles of another distribution E explicitly linked to F, in order to construct nonparametric kernel estimators of extreme conditional expectiles. We analyze the asymptotic properties of our estimators in the context of conditional heavy-tailed distributions. Applications to simulated data and real insurance data are provided.
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https://hal.archives-ouvertes.fr/hal-02114255
Contributor : Antoine Usseglio-Carleve <>
Submitted on : Friday, May 10, 2019 - 9:46:35 AM
Last modification on : Thursday, November 19, 2020 - 1:04:02 PM

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  • HAL Id : hal-02114255, version 2

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Stéphane Girard, Gilles Stupfler, Antoine Usseglio-Carleve. Nonparametric extreme conditional expectile estimation. 2019. ⟨hal-02114255v2⟩

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