2014/08/02 by David Gerard, Peter D. Hoff, Peter Hoff · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #Equivariant map #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Minimax #Pure mathematics #Tensor decomposition and applications #math.ST #msc:62C20 #msc:62F10 #msc:62F15 #msc:62H12 #stat.TH
paper · pdf · doi:10.1016/j.jmva.2015.01.020
published as Journal of Multivariate Analysis 137 (2015) 32--49
arxiv created 2014/08/02 · openalex publication_date 2015/02/07 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Inference about dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods for inference in the array normal model have appeared in the literature, but there have not been any results concerning the optimality properties of such estimators. In this article, we obtain results for the array normal model that are analogous to some classical results concerning covariance estimation for the multivariate normal model. We show that under a lower triangular product group, a uniformly minimum risk equivariant estimator (UMREE) can be obtained via a generalized Bayes procedure. Although this UMREE is minimax and dominates the MLE, it can be improved upon via an orthogonally equivariant modification. Numerical comparisons of the risks of these estimators show that the equivariant estimators can have substantially lower risks than the MLE.