  The classical multivariate extreme-value theory concerns the modeling of
extremes in a multivariate random sample, suggesting the use of max-stable
distributions. In this work, the classical theory is extended to the case where
aggregated data, such as maxima of a random number of observations, are
considered. We derive a limit theorem concerning the attractors for the
distributions of the aggregated data, which boil down to a new family of
max-stable distributions. We also connect the extremal dependence structure of
classical max-stable distributions and that of our new family of max-stable
distributions. By means of an inversion method, we derive a semiparametric
composite-estimator for the extremal dependence of the unobservable data,
starting from a preliminary estimator of the extremal dependence of the
aggregated data. Furthermore, we develop the large-sample theory of the
composite-estimator and illustrate its finite-sample performance via a
simulation study.
