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.

翻译：在将多元极值统计应用于分析由多元随机向量定义的复合事件尾部风险时，通常假设所有维度共享相同的极值指数。虽然此类假设可使用Wald型检验进行测试，但随着维度的增加，此类检验的性能会下降。本文提出了在高维设置下比较极值指数的新颖检验方法，适用于弱和一般的横截面尾部相依情形。我们建立了所提检验的渐近性质。在模拟中，所提检验在高维场景下显著优于现有方法。我们通过两个先前被假定在所有维度上具有相同极值指数的数据集，展示了所提检验的实际应用。