This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of rank-transformed variables, thereby quantifying the behavior of one variable when the other takes extreme values. We investigate the theoretical asymptotic behavior of the associated estimator. The effectiveness of the approach is demonstrated through an extensive simulation study. In addition, we discuss the use of the proposed coefficient for the detection of causal effects in extreme events. Finally, we apply the method to an oceanographic dataset, where the results highlight the strong asymmetric nature of extreme events and identify the dominant directions of extremal influence among key oceanographic variables. As a directional measure of tail dependence, our approach provides a natural tool for exploring causal-effect relationships in extreme-value settings.

翻译：本文提出了一种新度量，用于量化两个变量间极端事件的方向依赖性。该方法通过研究秩变换变量的条件尾部期望来捕捉非对称尾部依赖，从而揭示当一个变量取极端值时另一变量的变化行为。我们探讨了相关估计量的理论渐近性质，并通过大量仿真研究验证了其有效性。此外，本文讨论了所提系数在检测极端事件因果效应中的应用。最后，我们将该方法应用于海洋学数据集，结果凸显了极端事件的强非对称性，并识别了关键海洋变量间极端影响的主导方向。作为尾部依赖的方向性度量，该方法为探索极值情景下的因果关系提供了一种自然工具。