  The main approach to inference for multivariate extremes consists in
approximating the joint upper tail of the observations by a parametric family
arising in the limit for extreme events. The latter may be expressed in terms
of componentwise maxima, high threshold exceedances or point processes,
yielding different but related asymptotic characterizations and estimators. The
present paper clarifies the connections between the main likelihood estimators,
and assesses their practical performance. We investigate their ability to
estimate the extremal dependence structure and to predict future extremes,
using exact calculations and simulation, in the case of the logistic model.
