Extreme $$L^p$$ L p -quantile Kernel Regression

Stéphane Girard (), Gilles Stupfler () and Antoine Usseglio-Carleve ()
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Stéphane Girard: University of Grenoble-Alpes, Inria, CNRS, Grenoble INP, LJK
Gilles Stupfler: University of Rennes, Ensai, CNRS, CREST - UMR 9194
Antoine Usseglio-Carleve: University of Grenoble-Alpes, Inria, CNRS, Grenoble INP, LJK

A chapter in Advances in Contemporary Statistics and Econometrics, 2021, pp 197-219 from Springer

Abstract: Abstract Quantiles are recognized tools for risk management and can be seen as minimizers of an $$L^1$$ L 1 -loss function, but do not define coherent risk measures in general. Expectiles, meanwhile, are minimizers of an $$L^2$$ L 2 -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 $$L^p$$ L p -quantiles. We propose here to construct kernel estimators of extreme conditional $$L^p$$ L p -quantiles. We study their asymptotic properties in the context of conditional heavy-tailed distributions, and we show through a simulation study that taking $$p \in (1,2)$$ p ∈ ( 1 , 2 ) may allow to recover extreme conditional quantiles and expectiles accurately. Our estimators are also showcased on a real insurance data set.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-73249-3_11

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DOI: 10.1007/978-3-030-73249-3_11

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