Some Inference Problems Associated with the Complex Multivariate Normal Distribution

摘要

Consider k = q+1 complex multivariate normal populations with the same variance-covariance matrix but with different means. The problem of the number of discriminant functions needed to discriminate among the k-populations is considered and shown to be equivalent to the rank of the mean-space. A test for this dimensionality being R is presented. Also developed is the statistic for testing the goodness of fit of a single hypothetical discriminant function. As in the case of the real normal populations, the test statistic for this single hypothetical function is presented as the product of two independent factors, whose distributions are given; one measuring the direction aspect of the hypothetical function, and the other measures the collinearity aspect that is the necessity of only one function. Also included is the Bartlett decomposition of a complex Wishart matrix and some results pertaining to the coherence of complex random variables. (Author)