High dimensional inference for extreme value indices

Liujun Chen; Chen Zhou

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arXiv · 2407.20491

High dimensional inference for extreme value indices

Liujun Chen·Chen Zhou

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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.

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BibTeX RIS

Liujun Chen, Chen Zhou. 2024-07-30. High dimensional inference for extreme value indices. https://arxiv.org/abs/2407.20491

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