ON DOMAINS OF ATTRACTION OF MULTIVARIATE EXTREME-VALUE DISTRIBUTIONS UNDER ABSOLUTE CONTINUITY

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