A test to determine the multivariate normality of a data set

A test is described for multivariate normality that is useful in pattern recognition. The test is based on the Friedman-Rafsky (1979) multivariate extension of the Wald-Wolfowitz runs test. The test data are combined with a multivariate swarm of points following the normal distribution generated with mean vector and covariance matrix estimated from the test data. The minimal spanning tree of this resultant ensemble of points is computed and the count of the interpopulation edges in the minimal spanning tree is used as a test statistic. The simulation studied both the null case of the test and one simple deviation from normality. Two conclusions are made from this study. First, the test can be conservatively applied by using the asymptotic normality of the test statistic, even for small sample sizes. Second, the power of the test appears reasonable, especially in high dimensions. Monte Carlo experiments were performed to determine if the test is reliable in high dimensions with moderate sample size. The method is compared to other such tests available in the literature.<>