Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure

JOURNAL OF MULTIVARIATE ANALYSIS

卷:143

Article

Ros, Beata¹  Bijma, Fetsje¹  de Munck, Jan C.²  de Gunst, Mathisca C. M.¹ 

[1] Vrije Univ Amsterdam, Fac Exact Sci, Dept Math, NL-1081 HV Amsterdam, Netherlands

[2] Vrije Univ Amsterdam, Med Ctr, Dept Phys & Med Technol, NL-1081 HZ Amsterdam, Netherlands

关键词: Matrix normal model;    Covariance matrix;    Kronecker product structure;    Maximum likelihood estimation;    Existence and uniqueness of estimator;   

DOI  :  10.1016/j.jmva.2015.05.019

来源: Elsevier

【 摘 要 】

This paper deals with multivariate Gaussian models for which the covariance matrix is a Kronecker product of two matrices. We consider maximum likelihood estimation of the model parameters, in particular of the coVariance matrix. There is no explicit expression for the maximum likelihood estimator of a Kronecker product covariance matrix. We investigate whether the maximum likelihood estimator of the covariance matrix exists and whether it is unique. We consider models with general, with double diagonal, and with one diagonal Kronecker product covariance matrices, and find different results. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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