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Conference Papers Year : 2023

Analysis of variability in extremes with application in clustering of extreme events

Abstract

ANOVA is a widely used statistical technique to compare the means of several groups of independently sampled data. However, in some cases, examining tail behavior instead of the mean is more relevant. Therefore, we propose ANOVEX (ANalysis Of Variability in EXtremes), an analogue of ANOVA 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. We calculate within-group and between-group variances of extreme log-quantiles. We demonstrate that under the null hypothesis (H0) of 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, we propose to combine it with a decision tree algorithm for clustering of extremes, where each observation comes with K covariates. At each tree node, we apply the ANOVEX test for all possible splits of all covariates on data belonging to that node. The best splitting rule of the node is determined by the most significant test from ANOVEX. Once a large tree is built, we apply pruning by fusing two leaves if the best test statistic of their common parent is not significant. We apply this ANOVEX-tree algorithm to examples with K=1 covariate, as well as a real data example of wildfire burnt areas in the US with more than 500,000 samples and over 30 covariates.
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Dates and versions

hal-04170189 , version 1 (25-07-2023)

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  • HAL Id : hal-04170189 , version 1

Cite

Chen Yan, Stéphane Girard, Thomas Opitz, Antoine Usseglio-Carleve. Analysis of variability in extremes with application in clustering of extreme events. EVA 2023 - 13th International Conference on Extreme Value Analysis, Probabilistic and Statistical Models and their Applications, Jun 2023, Milan, Italy. ⟨hal-04170189⟩
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