High dimensional inference for extreme value indices
Abstract
When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be tested using a Wald-type test, the performance of such a test deteriorates as the dimensionality increases. This paper introduces novel tests for comparing extreme value indices in highdimensional settings, under both weak and general cross-sectional tail dependence. We establish the asymptotic behavior of the proposed tests. The proposed tests significantly outperform existing methods in high-dimensional scenarios in simulations. We demonstrate real-life applications of the proposed tests for two datasets previously assumed to have identical extreme value indices across all dimensions.
Cite
@article{arxiv.2407.20491,
title = {High dimensional inference for extreme value indices},
author = {Liujun Chen and Chen Zhou},
journal= {arXiv preprint arXiv:2407.20491},
year = {2026}
}