  Multivariate extreme value statistical analysis is concerned with
observations on several variables which are thought to possess some degree of
tail-dependence. In areas such as the modeling of financial and insurance
risks, or as the modeling of spatial variables, extreme value models in high
dimensions (up to fifty or more) with their statistical inference procedures
are needed. In this paper, we consider max-stable models for which the spectral
random vectors have absolutely continuous distributions. For random samples
with max-stable distributions we provide quasi-explicit analytical expressions
of the full likelihoods. When the full likelihood becomes numerically
intractable because of a too large dimension, it is however necessary to split
the components into subgroups and to consider a composite likelihood approach.
For random samples in the max-domain of attraction of a max-stable
distribution, two approaches that use simpler likelihoods are possible: (i) a
threshold approach that is combined with a censoring scheme, (ii) a block
maxima approach that exploits the information on the occurrence times of the
componentwise maxima. The asymptotic properties of the estimators are given and
the utility of the methods is examined via simulation. The estimators are also
compared with those derived from the pairwise composite likelihood method which
has been previously proposed in the spatial extreme value literature.
