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Book Sections Year : 2021

Extreme Lp-quantile kernel regression

Abstract

Quantiles are recognized tools for risk management and can be seen as minimizers of an L1-loss function, but do not define coherent risk measures in general. Expectiles, meanwhile, are minimizers of an L2-loss function and define coherent risk measures; they have started to be considered as good alternatives to quantiles in insurance and finance. Quantiles and expectiles belong to the wider family of Lp-quantiles. We propose here to construct kernel estimators of extreme conditional Lp-quantiles. We study their asymptotic properties in the context of conditional heavy-tailed distributions and we show through a simulation study that taking p ∈ (1, 2) may allow to recover extreme conditional quantiles and expectiles accurately. Our estimators are also showcased on a real insurance data set.
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Dates and versions

hal-03182032 , version 1 (26-03-2021)

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Stéphane Girard, Gilles Stupfler, Antoine Usseglio-Carleve. Extreme Lp-quantile kernel regression. Advances in Contemporary Statistics and Econometrics, Springer, pp.197-219, 2021, ⟨10.1007/978-3-030-73249-3_11⟩. ⟨hal-03182032⟩
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