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Abstract
The partitioned linear model ℳ12 is considered together with the reduced counterparts ℳ2 and ℳ(2), which are free from nuisance parameters present in ℳ12. The conditions are established under which the best linear unbiased estimator of parametric functions in the reduced model ℳ2(ℳ(2)) preserves its optimality in ℳ12. Expressed in terms of orthogonality and linear sufficiency, the characterizations remain valid when the support of the reduced model ℳ2(ℳ(2)) is a proper subset of the support of ℳ12. Moreover, some relationships between orthogonality and linear sufficiency are presented.