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On automatic bias reduction for extreme expectile estimation.

ABSTRACT: Expectiles induce a law-invariant risk measure that has recently gained popularity in actuarial and financial risk management applications. Unlike quantiles or the quantile-based Expected Shortfall, the expectile risk measure is coherent and elicitable. The estimation of extreme expectiles in the heavy-tailed framework, which is reasonable for extreme financial or actuarial risk management, is not without difficulties; currently available estimators of extreme expectiles are typically biased and hence may show poor finite-sample performance even in fairly large samples. We focus here on the construction of bias-reduced extreme expectile estimators for heavy-tailed distributions. The rationale for our construction hinges on a careful investigation of the asymptotic proportionality relationship between extreme expectiles and their quantile counterparts, as well as of the extrapolation formula motivated by the heavy-tailed context. We accurately quantify and estimate the bias incurred by the use of these relationships when constructing extreme expectile estimators. This motivates the introduction of classes of bias-reduced estimators whose asymptotic properties are rigorously shown, and whose finite-sample properties are assessed on a simulation study and three samples of real data from economics, insurance and finance.

Supplementary information

The online version contains supplementary material available at 10.1007/s11222-022-10118-x.

SUBMITTER: Girard S

PROVIDER: S-EPMC9362073 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

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On automatic bias reduction for extreme expectile estimation.

Girard Stéphane S Stupfler Gilles G Usseglio-Carleve Antoine A

Statistics and computing 20220809 4

Expectiles induce a law-invariant risk measure that has recently gained popularity in actuarial and financial risk management applications. Unlike quantiles or the quantile-based Expected Shortfall, the expectile risk measure is coherent and elicitable. The estimation of extreme expectiles in the heavy-tailed framework, which is reasonable for extreme financial or actuarial risk management, is not without difficulties; currently available estimators of extreme expectiles are typically biased and ...[more]

PMID: 35968040

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On automatic bias reduction for extreme expectile estimation.

Supplementary information

Publications

On automatic bias reduction for extreme expectile estimation.

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