I've published some R code on CRAN that will run a Gibbs sampler to draw from the posterior distribution of the Kronecker structured covariance matrix in the array normal model. This posterior is with respect to a (non-informative) prior induced by the right Haar measure over a product group of lower triangular matrices acting on the space of Kronecker structured covariance matrices. For any invariant loss function, any Bayes rule with respect to this prior will be the uniformly minimum risk equivariant estimator (UMREE) with respect to that loss. This R code will also calculate the UMREE under a multiway generalization of Stein's loss. This estimator dominates the maximum likelihood estimator uniformly over the over the entire parameter space of Kronecker structured covariance matrices.

Also available is a function that will calculate a (randomized) orthogonally invariant estimator of the Kronecker structured covariance matrix. This estimator dominates the UMREE under the product group of lower triangular matrices. Details of the methods may be found in

Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49. [Link to JMVA] [Link to arXiv] [bib]

I also provide a brief vignette on how to use the functions available in the R code. To download, simply type in R:

install.packages("tensr")

Alternatively, you can download it directly from CRAN.

Please provide us with questions or comments: David Gerard (dcgerard) or Peter Hoff (pdhoff) -- @uchicago.edu and @uw.edu, respectively.