Maximum likelihood estimation in the tensor normal model with a structured mean

There is a growing interest in the analysis of multi-way data.  In some studies theinference about the dependencies in three-way data is done using the third order tensornormal model, where the focus is on the estimation of the variance-covariance matrix whichhas a Kronecker product structure. Little attention is paidto the structure of the mean,though, there is a potential to improve the analysis by assuming a structured mean. Inthis paper, we introduce a 2-fold growth curve model by assuming a trilinear structure forthe mean in the tensor normal model and propose an algorithm for estimating parameters.Also, some direct generalizations are presented.