Estimation in multivariate linear models with Kronecker product and linear structures on the covariance matrices
(English)Manuscript (preprint) (Other academic)
This paper deals with models based on normally distributed random matrices. More specifically the model considered is X ∼ Np,q(M, Σ, Ψ) with mean M, a p×q matrix, assumed to follow a bilinear structure, i.e., E[X] = M = ABC, where A and C are known design matrices, B is unkown parameter matrix, and the dispersion matrix of X has a Kronecker product structure, i.e., D[X] = Ψ ⊗ Σ, where both Ψ and Σ are unknown positive definite matrices. The model may be used for example to model data with spatiotemporal relationships. The aim is to estimate the parameters of the model when, in addition, Σ is assumed to be linearly structured. In the paper, on the basis of n independent observations on the random matrix X, estimation equations in a flip-flop relation are presented and numerical examples are given.
Growth curve model, maximum likelihood estimators, estimation equations, flip-flop algorithm, Kronecker product structure, linear structure
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:liu:diva-78844ISRN: LiTH-MAT-R-2012/05-SEOAI: oai:DiVA.org:liu-78844DiVA: diva2:536189