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dc.contributor.authorBailey, Rosemary Anne
dc.contributor.authorFerreira, Sandra S.
dc.contributor.authorFerreira, Dario
dc.contributor.authorNunes, Celia
dc.identifier.citationBailey , R A , Ferreira , S S , Ferreira , D & Nunes , C 2016 , ' Estimability of variance components when all model matrices commute ' , Linear Algebra and its Applications , vol. 492 , pp. 144-160 .
dc.identifier.otherPURE: 230122910
dc.identifier.otherPURE UUID: 98593cf6-4008-4fe9-bdc7-fa648a1c4326
dc.identifier.otherScopus: 84950157195
dc.identifier.otherORCID: /0000-0002-8990-2099/work/39600101
dc.identifier.otherWOS: 000369562400014
dc.descriptionThis work was partially supported by national funds of FCT - Foundation for Science and Technology under UID/MAT/00212/2013.en
dc.description.abstractThis paper deals with estimability of variance components in mixed models when all model matrices commute. In this situation, it is well known that the best linear unbiased estimators of fixed effects are the ordinary least squares estimators. If, in addition, the family of possible variance-covariance matrices forms an orthogonal block structure, then there are the same number of variance components as strata, and the variance components are all estimable if and only if there are non-zero residual degrees of freedom in each stratum. We investigate the case where the family of possible variance-covariance matrices, while still commutative, no longer forms an orthogonal block structure. Now the variance components may or may not all be estimable, but there is no clear link with residual degrees of freedom. Whether or not they are all estimable, there may or may not be uniformly best unbiased quadratic estimators of those that are estimable. Examples are given to demonstrate all four possibilities.
dc.relation.ispartofLinear Algebra and its Applicationsen
dc.rights© 2015, Elsevier Inc. All rights reserved. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at /
dc.subjectAnalysis of varianceen
dc.subjectMixed modelen
dc.subjectOrthogonal block structureen
dc.subjectQA Mathematicsen
dc.titleEstimability of variance components when all model matrices commuteen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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