Estimability of variance components when all model matrices commute
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This 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.
Bailey , 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 . DOI: 10.1016/j.laa.2015.11.002
Linear Algebra and its Applications
© 2015, Publisher / the Author(s). 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 www.sciencedirect.com / https://dx.doi.org/10.1016/j.laa.2015.11.002
This work was partially supported by national funds of FCT - Foundation for Science and Technology under UID/MAT/00212/2013.
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