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Nonparametric extreme conditional expectile estimation

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HAL Id: hal-02186705

https://hal.inria.fr/hal-02186705

Submitted on 17 Jul 2019

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Nonparametric extreme conditional expectile estimation

Stéphane Girard, Gilles Stupfler, Antoine Usseglio-Carleve

To cite this version:

Stéphane Girard, Gilles Stupfler, Antoine Usseglio-Carleve. Nonparametric extreme conditional ex-pectile estimation. EVA 2019 - 11th International Conference on Extreme Value Analysis, Jul 2019, Zagreb, Croatia. pp.1. �hal-02186705�

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Nonparametric extreme conditional expectile estimation

Stéphane Girard1, Gilles Stupfler2, Antoine Usseglio-Carleve3

Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France1,3, University of Nottingham, School of Mathematical Sciences, Nottingham NG7 2RD, United

Kingdom2

stephane.girard@inria.fr1, Gilles.Stupfler@nottingham.ac.uk2, antoine.usseglio-carleve@inria.fr3

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 condi-tional expectiles. In this talk, we propose nonparametric estimators of extreme condicondi-tional expectiles based on kernel smoothing techniques. We analyze the asymptotic properties of our estimators in the context of conditional heavy-tailed distributions. Applications to simulated and real data are provided.

References

[1] Daouia, A., Girard, S., and Stupfler, G., Estimation of tail risk based on extreme expectiles, Journal of the Royal Statistical Society: Series B, 2018

[2] Usseglio-Carleve, A., Estimation of conditional extreme risk measures from heavy-tailed elliptical random vectors, Electronic Journal of Statistics, 2018

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