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Upper Bounds for the Euclidean Distances Between the BLUEs Under the Partitioned Linear Fixed Model and the Corresponding Mixed Model
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Permissible Covariance Structures for Simultaneous Retention of BLUEs in Small and Big Linear Models
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Further remarks on permissible covariance structures for simultaneous retention of BLUEs in linear models
We consider the partitioned linear model M12(V0) = { y, X1β1 + X2 β2, V0 } and the corresponding small model M1(V0) = { y, X1β1 , V0 } . We define the set V1/12 of nonnegative definite matrices V such that every representation of the best linear unbiased estimator, BLUE, of μ1 = X1β1 under M12(V0) remains BLUE under M12(V) . Correspondingly, we can characterize the set V1 of matrices V such that every BLUE of μ1 = X1β1 under M1(V0) remains BLUE under M1(V). In this paper we focus on the mutual relations between the sets V1 and V1/12 .