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

An asymptotic total variation test for copulas