A0618
Title: ANOVEX: Analysis of variability for heavy-tailed extremes
Authors: Stephane Girard - Inria (France)
Thomas Opitz - BioSP, INRA (France)
Antoine Usseglio-Carleve - Avignon Université (France) [presenting]
Abstract: Analysis of variance (ANOVA) is commonly employed to assess differences in the means of independent samples. However, it is unsuitable for evaluating differences in tail behaviour, especially when means do not exist or empirical estimation of moments is inconsistent due to heavy-tailed distributions. An ANOVA-like decomposition is proposed 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. Building on the assumption of regular variation, a test is introduced for significant tail differences among multiple independent samples and its asymptotic distribution is derived. The theoretical behavior is investigated by the test statistics for the case of two samples, each following a Pareto distribution, and explore strategies for setting hyperparameters in the test procedure. To demonstrate the finite-sample performance, simulations highlight generally reliable test behavior for a wide range of 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 at rain gauges in Germany.
