Approximations to the Distributions of the Likelihood Ratio Statistics for Testing Certain Structures on the Covariance Matrices of Real Multivariate Normal Populations

Abstract
In this report, the authors approximated the distributions of the likelihood ratio statistics for testing certain hypotheses on the covariance matrices of the multivariate normal populations by using suitable Pearson type distributions. The hypotheses that are considered include the hypotheses of sphericity, multiple homogeneity of covariance matrices and multiple independence. Using these approximations, tables of percentage points of the distributions considered are constructed. The accuracy of these tables is sufficient for practical purposes.

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