Generalized Cramér-von Mises goodness-of-fit tests for multivariate distributions

A class of statistics for testing the goodness-of-fit for any multivariate continuous distribution is proposed. These statistics consider not only the goodness-of-fit of the joint distribution but also the goodness-of-fit of all marginal distributions, and can be regarded as generalizations of the multivariate Cramér-von Mises statistic. Simulation shows that these generalizations, using the Monte Carlo test procedure to approximate their finite-sample p-values, are more powerful than the multivariate Kolmogorov-Smirnov statistic.