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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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03182032
Contributor : Gilles Stupfler <>
Submitted on : Friday, March 26, 2021 - 9:58:03 AM
Last modification on : Thursday, May 6, 2021 - 5:16:58 PM

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  • HAL Id : hal-03182032, version 1

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Stéphane Girard, Gilles Stupfler, Antoine Usseglio-Carleve. Extreme Lp-quantile kernel regression. 2021. ⟨hal-03182032⟩

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