When applying multivariate extreme values 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 a novel test for testing extreme value indices in a high dimensional setting. We show the asymptotic behavior of the test statistic and conduct simulation studies to evaluate its finite sample performance. The proposed test significantly outperforms existing methods in high dimensional settings. We apply this test to examine 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型检验进行验证，但随着维度的增加，此类检验的性能会下降。本文提出了一种在高维设置中检验极值指数的新方法。我们证明了检验统计量的渐近性质，并通过模拟研究评估了其有限样本性能。所提出的检验在高维设置中显著优于现有方法。我们应用该检验方法分析了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。