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

Beata Roś, Fetsje Bijma, Jan C. de Munck and Mathisca C.M. de Gunst

Journal of Multivariate Analysis, 2016, vol. 143, issue C, 345-361

Abstract: 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.

Keywords: Matrix normal model; Covariance matrix; Kronecker product structure; Maximum likelihood estimation; Existence and uniqueness of estimator (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.jmva.2015.05.019

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