Full likelihood inference for max-stable data

We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation 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 dramatic computational time improvements with respect to a direct computation of the likelihood. Strategies to further reduce the computational burden are also discussed.