Estimating the limit distribution of multivariate extremes

Consider a random sample from a multivariate distribution F(x) which is in the domain of attraction of a multivariate extreme value distribution G(x). Based on we construct an empirical measure which is a consistent estimator for — log G. In an appendix, we explore a second order strengthening of the standard multivariate domain of attraction condition and under this second order condition, we prove our estimator is asymptotically normal in a suitably strong sense