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Conference Papers Year : 2021

Extreme expectile regression: theory and applications

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 signicantly 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 work, we firstly construct nonparametric kernel estimators of extreme conditional expectiles. We analyze the asymptotic properties of our estimators in the context of conditional heavy-tailed distributions, and realize that such a nonparametric approach is no longer suitable when the covariate dimension is too large. We thus also build a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise; our approach is supported by general results of independent interest on residual-based extreme value estimators in heavy-tailed regression models, and is intended to cope with co- variates having a large but fixed dimension. We demonstrate how our results can be applied to a wide class of important examples, among which linear models, single-index models as well as ARMA and GARCH time series models. Our estimators are showcased on a numerical simulation study and on real sets of actuarial and financial data.
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Dates and versions

hal-03301456 , version 1 (27-07-2021)

Identifiers

  • HAL Id : hal-03301456 , version 1

Cite

Antoine Usseglio-Carleve, Stéphane Girard, Gilles Stupfler. Extreme expectile regression: theory and applications. EVA 2021 - 12th International Conference on Extreme Value Analysis, Jun 2021, Edinburgh / Virtual, United Kingdom. ⟨hal-03301456⟩
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