Asymptotic Distributions of the Likelihood Ratio Test Statistics for Covariance Structures of the Complex Multivariate Normal Distribution

摘要

IN this paper, the authors obtained asymptotic expressions for the null and nonnull distributions of the likelihood ratio test statistic for multiple independence when the underlying distribution is complex multivariate normal. The authors also derived asymptotic null distribution of the likelihood ratio test statistic for homogeneity of the covariance matrices of several complex multivariate normal populations; asymptotic expressions are also obtained for the nonnull case when we have two populations. The expressions obtained in this paper are in terms of beta series. (Author)