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Max-stable distributions and processes are important models for extremeevents and the assessment of tail risks. The full, multivariate likelihood of aparametric max-stable distribution is complicated and only recent advancesenable its use. The asymptotic properties of the maximum likelihood estimatorin multivariate extremes are mostly unknown. In this paper we provide naturalconditions on the exponent function and the angular measure of the max-stabledistribution that ensure asymptotic normality of the estimator. We show theeffectiveness of this result by applying it to popular parametric models inmultivariate extreme value statistics and to the most commonly used families ofspatial max-stable processes.

Asymptotic properties of the maximum likelihood estimator for multivariate extreme value distributions