Abstract
AbstractA sample is taken from a continuous multivariate distribution. The problem is to test the hypothesis that the unknown joint cumulative distribution function is equal to a completely specified function. The observed data are transformed so that the hypothesis being tested is that the distribution is uniform over a unit hypercube. If only neighboring alternatives are considered, it is shown that the numbers of observations falling in a gradually increasing number of subcubes are asymptotically sufficient. It is shown that for all asymptotic probability calculations, we can assume that the joint distribution of the numbers of observations can be considered to be the distribution of slightly rounded off normal random variables. Tests based on these facts are constructed.
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