On domains of attraction of multivariate extreme value distributions under absolute continuity

The paper gives sufficient conditions for domains of attraction of multivariate extreme value distributions. Under the assumption of absolute continuity of a multivariate distribution, the criteria enable one to examine, by using limits of some rescaled conditional densities, whether the distribution belongs to the domain of attraction of some multivariate extreme value distribution. If this is the case, the criteria also determine how to construct such an extreme value distribution. Unlike the criterion given by de Haan and Resnick [1987, Stochastic Process. Appl. 25 83-93], the criteria are easily applicable even when the marginal tails are not Pareto-like. (C) 1997 Academic Press.