Extreme-value copulas arise in the asymptotic theory for componentwise maxima
of independent random samples. An extreme-value copula is determined by its
Pickands dependence function, which is a function on the unit simplex subject
to certain shape constraints that arise from an integral transform of an
underlying measure called spectral measure. Multivariate extensions are
provided of certain rank-based nonparametric estimators of the Pickands
dependence function. The shape constraint that the estimator should itself be a
Pickands dependence function is enforced by replacing an initial estimator by
its best least-squares approximation in the set of Pickands dependence
functions having a discrete spectral measure supported on a sufficiently fine
grid. Weak convergence of the standardized estimators is demonstrated and the
finite-sample performance of the estimators is investigated by means of a
simulation experiment.Comment: 26 pages; submitted; Universit\'e catholique de Louvain, Institut de
statistique, biostatistique et sciences actuarielle
