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, such procedures are 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：在环境规划、灾害建模和水文学等众多实际应用中，二元变量的极值依赖建模具有重要意义。现有方法大多基于二元正则变差框架，且已有大量文献致力于估计该框架下的依赖结构。然而，此类方法仅适用于呈现渐近依赖的变量，而实践中常观测到渐近独立现象。本文研究所谓的"角依赖函数"，该函数概括了渐近独立变量的极值依赖结构。直至近期，该函数仅有逐点估计量可用。我们提出了一系列全局估计量，并通过系统模拟研究及英国英格兰北部河流流量数据的案例研究，将其与另一种新近提出的全局估计技术进行比较。