Advisor: Peter Hoff
Estimation and testing of the dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with Kronecker structured covariance matrices. Maximum likelihood and Bayesian methods for estimation in the array normal model have appeared in the literature, but there have not been any results concerning the optimality properties of such estimators. Using the notions of equivariance, we will describe optimality results for the array normal model that are analogous to some classical results concerning covariance estimation for the multivariate normal model. Specifically, we find equivariant and minimax dominators of the MLE. If we have time, we will then review likelihood techniques and show that maximum likelihood estimation in the array normal model is analogous to a higher order version of the LQ decomposition, which we call the Incredible HOLQ. We will also address testing in the array normal model by developing a likelihood ratio test.