Mathmatics Colloquium: "Theory and Methods for Tensor Covariance Estimation"
4:10PM Neill 5W
Estimation and testing of the dependencies in a multiway data array, or tensor, can be made using the array normal model, which corresponds to the class of multivariate normal distributions with Kronecker structured, or separable, 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 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 maximum likelihood estimator. We then develop a higher-order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable covariance models.