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 Σ, and (iii) the problem of intraclass model for the covariance matrix Σ, when the column vectors of X are independently distributed as multivariate normal with covariance matrix Σ and E(X) = BξA,A and B being given matrices and ξ and Σ 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.