  Many applications in risk analysis, especially in environmental sciences,
require the estimation of the dependence among multivariate maxima. A way to do
this is by inferring the Pickands dependence function of the underlying
extreme-value copula. A nonparametric estimator is constructed as the sample
equivalent of a multivariate extension of the madogram. Shape constraints on
the family of Pickands dependence functions are taken into account by means of
a representation in terms of a specific type of Bernstein polynomials. The
large-sample theory of the estimator is developed and its finite-sample
performance is evaluated with a simulation study. The approach is illustrated
by analyzing clusters consisting of seven weather stations that have recorded
weekly maxima of hourly rainfall in France from 1993 to 2011.
