Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, this framework is only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called `angular dependence function'; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK.

翻译：摘要：双变量极值依赖的建模在广泛的实际应用中具有重要意义，包括环境规划、灾害建模和水文学。这些方法大多基于二元正则变异的框架，已有大量文献用于估计该框架下的依赖结构。然而，该框架仅适用于表现出渐近依赖的变量，尽管实践中常观察到渐近独立现象。本文考虑了所谓的"角依赖函数"；该量描述了渐近独立变量的极值依赖结构。直到最近，仅有角依赖函数的逐点估计器可用。我们引入了一系列全局估计器，并通过系统仿真研究以及针对英国英格兰北部河流流量数据的案例研究，将其与另一种近期提出的全局估计技术进行了比较。