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Published in:
2019 | OriginalPaper | Chapter
Orthogonal Block Structure and Uniformly Best Linear Unbiased Estimators
Authors : Sandra S. Ferreira, Dário Ferreira, Célia Nunes, Francisco Carvalho, João Tiago Mexia
Published in: Matrices, Statistics and Big Data
Publisher: Springer International Publishing
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Abstract
Models with orthogonal block structure, OBS, have variance covariance matrices that are linear combinations \(\sum _{j=1}^{m} \gamma _{j} Q_{j}\) of known pairwise orthogonal–orthogonal projection matrices that add up to I
n. We are interested in characterizing such models with least square estimators that are best linear unbiased estimator whatever the variance components, assuming that γ ∈ ∇≥, with ∇≥ the set of vectors with nonnegative components of a subspace ∇. This is an extension of the usual concept of OBS in which we require \(\boldsymbol {\gamma } \in \mathbb {R}^{m}_{\geq }.\) Thus as we shall see it is usual when we apply our results to mixed models.