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：对双变量变量的极值依赖性建模在环境规划、灾害建模和水文学等广泛的实际应用中至关重要。大多数方法基于双变量正则变异的框架，已有大量文献探讨该框架下依赖结构的估计。然而，该框架仅适用于表现出渐近依赖性的变量，尽管实践中常观察到渐近独立性。本文考虑所谓的“角依赖函数”，该量概括了渐近独立变量的极值依赖结构。直到近期，仅有角依赖函数的逐点估计方法可用。我们引入了一系列全局估计方法，并通过系统性模拟研究以及与另一种近期提出的全局估计技术的比较，结合英国英格兰北部河流流量数据的案例研究，进行了评估。