Multivariate Goodness of Fit Testing Using Two-Sample Nearest Neighbor Procedures

We consider the problem of multivariate goodness of fit testing. We develop a test based on generating data samples from the hypothesized null distribution and performing a series of two-sample tests of the actual data set against each of the generated data samples. We address the problem of correlation between the test statistics from the two-sample tests and provide a method of accounting for it when combining the p-values from each test using Fisher’s method. We also provide an alternative implementation of the test that does not require consideration of the aforementioned correlation. We provide power results via simulation for two different two-sample tests across a variety of cases with four different distributions in varying dimensions.