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A note on the equality of the BLUPs for new observations under two linear models. (English) Zbl 1229.15023
Summary: We consider two linear models, $${\mathcal L}_1$$ and $${\mathcal L}_2$$, say, with new unobserved future observations. We give necessary and sufficient conditions in the general situation, without any rank assumptions, that the best linear unbiased predictor (BLUP) of the new observation under the model $${\mathcal L}_1$$ continues to be BLUP also under the model $${\mathcal L}_2$$.

##### MSC:
 15A42 Inequalities involving eigenvalues and eigenvectors 62J05 Linear regression; mixed models 62H12 Estimation in multivariate analysis 62H20 Measures of association (correlation, canonical correlation, etc.)