Equivariant minimax dominators of the MLE in the array normal model

David Gerard and Peter Hoff

Journal of Multivariate Analysis, 2015, vol. 137, issue C, 32-49

Abstract: Inference about dependence 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.

Keywords: Bayesian estimation; Covariance estimation; Gibbs sampling; Stein’s loss; Tensor data (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X15000330
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:137:y:2015:i:c:p:32-49

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2015.01.020

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().