Chen, L. and Zhou, C. (2026). High-dimensional inference for extreme value indices Journal of the American Statistical Association.

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 article introduces novel tests for comparing extreme value indices in high-dimensional 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.