Girard S, Stupfler G, Usseglio-Carleve A. On automatic bias reduction for extreme expectile estimation.
STATISTICS AND COMPUTING 2022;
32:64. [PMID:
35968040 PMCID:
PMC9362073 DOI:
10.1007/s11222-022-10118-x]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 05/30/2022] [Indexed: 06/15/2023]
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.
Collapse