In this article we consider a pq-dimensional random vector x distributed normally with mean vector θ and the covariance matrix Λ, assumed to be positive definite. On the basis of N independent observations on the random vector x, we wish to estimate parameters and test the hypothesis H: Λ = Ψ ⊗Σ, where Ψ = (ψ ij ) : q × q and Σ = (σ ij ) : p × p, and Λ = (ψ ij Σ), the Kronecker product of Ψ and Σ. That is instead of
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