Hashorva, EnkelejdPadoan, Simone A.Rizzelli, Stefano2020-08-122020-08-122020-08-12202110.1111/sjos.12463https://infoscience.epfl.ch/handle/20.500.14299/170798WOS:000552748400001The 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. Using 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.Statistics & ProbabilityMathematicsextremal dependenceextreme-value copulainverse problemmultivariate max-stable distributionnonparametric estimationpickands dependence functionnonparametric-estimationdependenceinferencetext::journal::journal article::research article