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Estimation in General Multivariate Linear Models with Kronecker Product Covariance Structure
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2008 (English)Report (Other academic)
Abstract [en]

In this article models based on pq-dimensional normally distributed random vectors x are studied with a mean vec(ABC), where A and C

are known matrices, and a separable covariance matrix $\psi\otimes \Sigma$, where both $\Psi$ and $\Sigma$ are positive definite and except the estimability condition $\psi_{qq} = 1$, unknown. The model may among others be applied when spatial-temporal relationships exist. On the basis of n independent observations on the random vector x, we wish to estimate the parameters of the model. In the paper estimation equations for obtaining maximum likelihood estimators are presented. It is shown that there exist only one solution to these equations. Likelihood equations are also considered when $FBG = 0$, with F and G known. Moreover, the likelihood ratio test for testing $FBG = 0$ against $FBG\neq = 0$ is considered.

Place, publisher, year, edition, pages
Centre of Biostochastics, Umeå, Sweden , 2008.
Series
Research Report, ISSN 1651-8543 ; 1
Keyword [en]
Growth Curve model, estimation equations, Kronecker product structure, maximum likelihood estimators, separable covariance.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-13980OAI: oai:DiVA.org:su-13980DiVA: diva2:180500
Available from: 2008-05-23 Created: 2008-05-23Bibliographically approved

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http://biostochastics.slu.se/publikationer/dokument/Report2008_01.pdf
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