Abstract
We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic expectation-maximization algorithm, which combines statistical and computational efficiency in high dimensions. The good performance of this methodology is demonstrated by simulation based on the popular logistic and Brown-Resnick models, and it is shown to provide computational time improvements with respect to a direct computation of the likelihood. Strategies to further reduce the computational burden are also discussed.