A note on the equality of the BLUPs for new observations under two linear models

Abstract

We consider two linear models, L_1 and 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 the model L_1 continues to be BLUP also under the model L_2.