A0653
Title: Analysis of variability in extremes
Authors: Chen Yan - INRAE/Inria (France) [presenting]
Stephane Girard - Inria (France)
Thomas Opitz - INRA (France)
Antoine Usseglio-Carleve - Avignon Université (France)
Abstract: ANOVA is a widely used statistical technique to compare the means of several groups of independently sampled data. However, examining tail behaviour instead of the mean is more relevant in some cases. Therefore, ANOVEX (ANalysis Of Variability in EXtremes), an analogue of ANOVA, is proposed to compare the behaviour of extremes across J>1 groups. The ANOVEX test involves selecting a number L>1 of extreme quantiles within each group, estimated using methods such as the Weissman estimator. Within-group and between-group variances of extreme log quantiles are calculated. It is demonstrated that under the null hypothesis of the same behaviour across groups, the ratio of these variances converges to a chi-square distribution with J-1 degrees of freedom after normalization. To further enhance the applicability of ANOVEX, it is proposed to combine it with a decision tree algorithm for clustering of extremes, where each observation comes with K covariates. At each tree node, the ANOVEX test is applied for all possible splits of all covariates on data belonging to that node. The most significant test from ANOVEX determines the best splitting rule of the node. Once a large tree is built, pruning by fusing two leaves is applied if the best test statistic of their common parent is not significant. This ANOVEX-tree algorithm is applied to examples with K=1 covariate and a real data example of wildfire-burnt areas in the US with more than 500,000 samples and over 30 covariates.
