We propose a coefficient that measures dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in significant ways: 1) it is designed to measure dependence between curves, 2) it focuses only on extreme curves. The new coefficient is derived within the framework of regular variation in Banach spaces. A consistent estimator is proposed and justified by an asymptotic analysis and a simulation study. The usefulness of the new coefficient is illustrated on financial and and climate functional data.

翻译：本文提出了一种度量函数配对样本间依赖关系的系数。该系数具有与皮尔逊相关系数相似的性质，但在重要方面存在差异：1）专门设计用于度量曲线间的依赖关系；2）仅关注极端曲线。新系数是在巴拿赫空间正则变差框架下推导得出的。我们提出了一致估计量，并通过渐近分析和模拟研究验证了其有效性。最后，通过金融与气候函数型数据的应用实例展示了新系数的实用价值。