Estimation of the angular density in bivariate generalized Pareto models

We investigate a method to estimate the angular density non-parametrically in bivariate generalized Pareto models. The angular density can be used as a visual tool to gain a first insight into the tail-dependence structure of given data. We derive a representation of the angular density by means of the Pickands density and use it to construct our estimator. The estimator is asymptotically normal under certain regularity conditions. We also test it with simulated data and give an application to a real hydrological data set. Finally, we show that our estimator cannot be transferred directly to higher dimensions.