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Preprints, Working Papers, ... Year : 2024

ANOVEX: ANalysis Of Variability for heavy-tailed EXtremes

Abstract

Analysis of variance (ANOVA) tests for differences in the means of independent samples but is unsuitable for evaluating differences in tail behaviour, especially when means do not exist or empirical estimation of means or higher moments is inconsistent due to heavy-tailed distributions. Here, we propose an ANOVA-like decomposition to analyse 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 behaviour 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 behaviour 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.
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Dates and versions

hal-04200300 , version 1 (08-09-2023)
hal-04200300 , version 2 (31-05-2024)

Identifiers

  • HAL Id : hal-04200300 , version 2

Cite

Stéphane Girard, Thomas Opitz, Antoine Usseglio-Carleve. ANOVEX: ANalysis Of Variability for heavy-tailed EXtremes. 2024. ⟨hal-04200300v2⟩
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