This research will examine goodness-of-fit tests for multivariate data modeled using distribution-free or nonparametric models. The small sample behavior of test statistics based on spacings will be investigated using Monte Carlo methods and will be compared to limiting distribution theoretical results. By constructing statistically equivalent blocks, test statistics can be extended to the multidimensional case. When trying to represent an underlying explanatory or descriptive model for real multivariate data, a crucial difficulty is to determine when a postulated model is adequate. The fewer the mathematical assumptions made initially, the more difficult in general to be sure that the model does represent the important features, but not any artifacts of a particular sample. Some mathematical theory has been developed for the case of an arbitrarily large sample; some theory has been developed when the data is assumed to follow a Gaussian (normal) distribution. This project will examine tests of model adequacy when the samples are not extremely large and at the same time the distribution cannot be assumed to be normal. The work will concentrate on multi- variate observations.
