Abstract
While analysis of variance (ANOVA) tests for differences in the means of independent samples, it is unsuitable for evaluating differences in tail behavior, especially when means do not exist or empirical estimation of means or higher moments is not consistent due to heavy-tailed distributions. Here, we propose an ANOVA-like decomposition to analyze tail variability, allowing for flexible representation of heavy tails through a set of user-defined extreme quantiles, possibly located outside the range of observations. Assuming regular variation, we introduce a test for significant tail differences across multiple independent samples and derive its asymptotic distribution. We investigate the theoretical behavior of the test statistics for the case of two samples, each following a Pareto distribution, and explore strategies for setting test hyperparameters. We conduct simulations that highlight generally reliable test behavior for a wide range of finite-sample situations. The test is applied to identify clusters of financial stock indices with similar extreme log-returns and to detect temporal changes in daily precipitation extremes in Germany.
Funding Statement
This work is part of the ANOVEX project funded by the French national research institutes INRAE and Inria within the scope of their collaborations on the topic of environmental risks. This work is further supported by the French National Research Agency (ANR) in the framework of the Investissements d’Avenir Program (ANR-15-IDEX-02). The first author acknowledges the support of the Chair “Stress Test, Risk Management and Financial Steering”, led by the French Ecole Polytechnique and its Foundation and sponsored by BNP Paribas.
Acknowledgments
The authors would like to warmly thank two anonymous referees, an Associate Editor and the Editor for their numerous very constructive comments that helped to improve the content and quality of this paper.
Citation
Stéphane Girard. Thomas Opitz. Antoine Usseglio-Carleve. "ANOVEX: ANalysis Of Variability for heavy-tailed EXtremes." Electron. J. Statist. 18 (2) 5258 - 5303, 2024. https://doi.org/10.1214/24-EJS2323
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