  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.
