Abstract

Under the multivariate model with linearly structured covariance matrix with unknown variance components and known mean parameters it is known that the maximum likelihood estimators (MLEs) of variance components have explicit representation if and only if the space of covariance matrix is a quadratic subspace.
 
In this talk, it will be shown, that the above result can be extended also for models with unknown mean parameters. Moreover, it will be proven that is such a model the projection of the MLE of unstructured covariance onto the space of structured matrices is still the MLEs as long as the estimated structure belongs to quadratic space.