Statistical inference for extreme extremile in heavy-tailed heteroscedastic regression model

Yu Chen, Mengyuan Ma and Hongfang Sun

Insurance: Mathematics and Economics, 2023, vol. 111, issue C, 142-162

Abstract: As a least squares analogue of quantiles, extremiles define a coherent risk measure determined by weighted expectations instead of tail probabilities. Estimating extremiles of heavy-tailed variables in a regression framework is a challenging task, especially for dependent cases. This paper develops some methods for the estimation of extreme conditional extremiles in the framework of heteroscedastic regression model with heavy-tail noises, specifically, direct and indirect methods based on the conditional extremile estimators for the residuals. We also construct corresponding bias-reduced estimators and investigate their asymptotic properties compared to the original versions. Our mathematical assumptions are satisfied in the mean-variance regression model and heteroscedastic single-index model, which makes it possible to apply our result in a series of important examples. We demonstrate our results through a simulation study and real sets of insurance and financial data analyses.

Keywords: Conditional extremiles; Extreme value theory; Heavy-tailed distribution; Heteroscedastic regression; Inference (search for similar items in EconPapers)
JEL-codes: C1 C13 C15 C51 G22 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:111:y:2023:i:c:p:142-162

DOI: 10.1016/j.insmatheco.2023.04.001

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