  We propose a new goodness-of-fit test for copulas, based on empirical copula
processes and their nonparametric bootstrap counterparts. The standard
Kolmogorov-Smirnov type test for copulas that takes the supremum of the
empirical copula process indexed by half spaces is extended by test statistics
based on the supremum of the empirical copula process indexed by partitions of
Ln rectangles with Ln slowly tending to infinity. Although the underlying
empirical process does not converge, it is proved that the p-values of our new
test statistic can be consistently estimated by the bootstrap. Simulations
confirm that the power of the new procedure is higher than the power of the
standard Kolmogorov-Smirnov test for copulas.
