Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack theoretical justification and statistical guarantees. On the other hand, extreme value theory provides the theoretical foundation for constructing asymptotically justified tests. We combine this theory with Kullback-Leibler divergence, a fundamental concept in information theory and statistics, to propose a test for equality of extremal dependence structures in practically relevant directions. Under suitable assumptions, we derive the limiting distributions of the proposed statistic under null and alternative hypotheses. Importantly, our test is fast to compute and easy to interpret by practitioners, making it attractive in applications. Simulations provide evidence of the power of our test. In a case study, we apply our method to show the strong impact of seasons on the strength of dependence between different aggregation periods (daily versus hourly) of heavy rainfall in France.

翻译：检验两个多元样本是否表现出相同的极值行为是环境与气候科学等多个领域的重要问题。尽管文献中存在多种临时性方法，但它们往往缺乏理论依据和统计保证。另一方面，极值理论为构建渐近合理的检验提供了理论基础。我们将该理论与信息论和统计学中的基本概念——Kullback-Leibler散度相结合，提出了一种针对实际相关方向上极值依赖结构相等性的检验方法。在适当假设下，我们推导了所提出统计量在原假设和备择假设下的极限分布。重要的是，我们的检验计算快速且易于从业者解释，使其在实际应用中具有吸引力。仿真实验证明了我们检验方法的效力。在案例研究中，我们应用该方法揭示了季节对法国强降雨不同聚合周期（日尺度与小时尺度）间依赖强度的显著影响。