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–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.