Estimating a Multidimensional Extreme-Value Distribution

Let F and G be multivariate probability distribution functions, each with equal one dimensional marginals, such that there exists a sequence of constants an > 0, n ∈ N, with [formula] for all continuity points (x1, ..., xd) of G. The distribution function G is characterized by the extreme-value index (determining the marginals) and the so-called angular measure (determining the dependence structure). In this paper, a non-parametric estimator of G, based on a random sample from F, is proposed. Consistency as well as asymptotic normality are proved under certain regularity conditions.