 General linear mixed model and signal extraction problem with constraintAzzouz Dermoune, Nadji Rahmania and Tianwen Wei Journal of Multivariate Analysis, 2012, vol. 105, issue 1, 311-321 Abstract: We consider a noisy observed vector y=x+u∈Rn. The unobserved vector x is a solution of a non-invertible linear system Ax=v, where v is a forcing term. A unique solution of the system is obtained by considering additional constraint on the vector x. This constraint is defined by a triple (β,F,A−), where β is a vector, F denotes a matrix whose range is equal to N(A) (the null space of A) and A− is a generalized inverse of A. Each triple (β,F,A−) defines the solution x=Fβ+A−v and the general linear mixed model y=Fβ+A−v+u. Given the covariance matrices of u and v, we will prove that the best linear unbiased predictor of x knowing y depends only on A. If β is a parameter and (F,A−) is given, then we will study the asymptotic behavior of the best linear estimator of β. If the constraint (β,F,A−) is not known, then we will estimate it using the data y. Some numerical results will be given. Keywords: Signal extraction; Generalized inverse; Asymptotic property; BLUE; BLUP; Auto-regressive model; Maximum likelihood estimator; Inverse problem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:105:y:2012:i:1:p:311-321 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2011.10.007 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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