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

B.P. Ros, F. Bijma, J.C. de Munck, M.C.M. de Gunst

Research output: Contribution to JournalArticleAcademicpeer-review

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.
Original languageEnglish
Article numberdoi.org/10.1016/j.jmva.2015.05.019
Pages (from-to)345-361
JournalJournal of Multivariate Analysis
Volume143
DOIs
Publication statusPublished - 2016

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Kronecker Product
Covariance Structure
Covariance matrix
Maximum Likelihood Estimator
Maximum likelihood
Existence and Uniqueness
Model
Maximum likelihood estimation
Multivariate Models
Gaussian Model
Maximum Likelihood Estimation
Uniqueness
Maximum likelihood estimator

Cite this

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title = "Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure",
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.",
author = "B.P. Ros and F. Bijma and {de Munck}, J.C. and {de Gunst}, M.C.M.",
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journal = "Journal of Multivariate Analysis",
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Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure. / Ros, B.P.; Bijma, F.; de Munck, J.C.; de Gunst, M.C.M.

In: Journal of Multivariate Analysis, Vol. 143, doi.org/10.1016/j.jmva.2015.05.019, 2016, p. 345-361.

Research output: Contribution to JournalArticleAcademicpeer-review

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AB - 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.

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