Testing some covariance structures under a growth curve model

This paper considers three types of problems: (i) the problem of independence of two sets, (ii) the problem of sphericity of the covariance matrix [Sigma], and (iii) the problem of intraclass model for the covariance matrix [Sigma], when the column vectors of X are independently distributed as multivariate normal with covariance matrix [Sigma] and E(X) = B[xi]A,A and B being given matrices and [xi] and [Sigma] being unknown. These problems are solved by the likelihood ratio test procedures under some restrictions on the models, and the null distributions of the test statistics are established.