Extreme value inference for heterogeneous power law data
Einmahl,John He,Y.
Einmahl,John
He,Y.
Abstract
We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, we consider a heterogeneous scales model where the asymptotic variance can be calculated explicitly. The primary tool for the proofs is the functional central limit theorem for a weighted tail empirical process. We also present asymptotic normality results for the extreme quantile estimator. A simulation study shows the good finite-sample behavior of our limit theorems. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.
Description
Publisher Copyright: © 2023 Institute of Mathematical Statistics.
Date
2023-06
Journal Title
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Volume Title
Publisher
Research Projects
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Keywords
Extreme value statistics, Functional central limit theorem, Heterogeneous scales model, Hill estimator, Nonidentical distributions, Weighted tail empirical process
Citation
Einmahl, J & He, Y 2023, 'Extreme value inference for heterogeneous power law data', Annals of Statistics, vol. 51, no. 3, pp. 1331-1356. https://doi.org/10.1214/23-AOS2294
License
info:eu-repo/semantics/openAccess