Some bayes tests and their asymptotic properties for the multivariate,multisample goodness-of-fit problem

Independent samples are taken from C multivariate populations with continuous but unknown cumulative distribution function c.d.f.). The problem is to test the hypothesis that the C population c.d.f's are identical to a specified c.d.f. We approach this problem by first transforming the data so that the hypothesis being tested is that the common distribution is uniform over a unit hypercube. We then construct some Bayes tests and investigate their asymptotic properties. These tests are based on the asymptotic normality of the number of observations falling in the “asymptotically sufficient groupings”.