  Starting from the characterization of extreme-value copulas based on
max-stability, large-sample tests of extreme-value dependence for multivariate
copulas are studied. The two key ingredients of the proposed tests are the
empirical copula of the data and a multiplier technique for obtaining
approximate p-values for the derived statistics. The asymptotic validity of the
multiplier approach is established, and the finite-sample performance of a
large number of candidate test statistics is studied through extensive Monte
Carlo experiments for data sets of dimension two to five. In the bivariate
case, the rejection rates of the best versions of the tests are compared with
those of the test of Ghoudi, Khoudraji and Rivest (1998) recently revisited by
Ben Ghorbal, Genest and Neslehova (2009). The proposed procedures are
illustrated on bivariate financial data and trivariate geological data.
