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This paper deals with multivariate Gaussian models for which the covariancematrix is a Kronecker product of two matrices. We consider maximum likelihoodestimation of the model parameters, in particular of the covariance matrix.There is no explicit expression for the maximum likelihood estimator of aKronecker product covariance matrix. The main question in this paper is whetherthe maximum likelihood estimator of the covariance matrix exists and if it isunique. The answers are different for different models that we consider.

Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure