Estimation equations for multivariate linear models with Kronecker structured covariance matrices

Anna Szczepańska-Álvarez, Chengcheng Hao, Yuli Liang and Dietrich von Rosen

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 16, 7902-7915

Abstract: The aim of the paper is to determine maximum-likelihood estimation equations. Observations follow a multivariate normal distribution, Xi∼Np,q(μ,Ψ,Σ)$\mbox{\boldmath $ {\bf X}$}_i \sim N_{p,q}(\mbox{\boldmath $ {\bf \mu }$},\mbox{\boldmath $ {\bf \Psi }$},\mbox{\boldmath $ {\bf \Sigma }$})$, where D[Xi]=Σ⊗Ψ$D[\mbox{\boldmath $ {\bf X}$}_i]= \mbox{\boldmath $ {\bf \Sigma }$}\otimes \mbox{\boldmath $ {\bf \Psi }$}$, Ψ$\mbox{\boldmath $ {\bf \Psi }$}$ and Σ$\mbox{\boldmath $ {\bf \Sigma }$}$ describe the unknown covariance structure between rows and columns of Xi$\mbox{\boldmath $ {\bf X}$}_i$, respectively. Imposing restrictions on Ψ$\mbox{\boldmath $ {\bf \Psi }$}$ and Σ$\mbox{\boldmath $ {\bf \Sigma }$}$ four types of covariance structures will be considered.

Date: 2017
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DOI: 10.1080/03610926.2016.1165852

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