High dimensional inference for extreme value indices

TL;DR

This paper introduces new statistical tests for comparing extreme value indices in high-dimensional data, addressing the limitations of existing methods as dimensionality increases, and demonstrates their effectiveness through simulations and real data applications.

Contribution

The paper develops novel tests for high-dimensional extreme value index comparison that outperform existing methods and establish their asymptotic properties.

Findings

Proposed tests outperform existing methods in high-dimensional simulations

Tests are effective under weak and general tail dependence

Real data applications confirm practical utility

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.