Skip to Main content Skip to Navigation
Journal articles

Nonparametric extreme conditional expectile estimation

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.
Complete list of metadata

Cited literature [53 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02114255
Contributor : Stephane Girard <>
Submitted on : Tuesday, June 30, 2020 - 6:56:35 PM
Last modification on : Wednesday, March 10, 2021 - 3:04:06 PM

File

hal_revised.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Stephane Girard, Gilles Stupfler, Antoine Usseglio-Carleve. Nonparametric extreme conditional expectile estimation. Scandinavian Journal of Statistics, Wiley, In press, ⟨10.1111/sjos.12502⟩. ⟨hal-02114255v3⟩

Share

Metrics

Record views

220

Files downloads

171