A note on the equality of the BLUPs for new observations under two linear models. (English) Zbl 1229.15023

Haslett, Stephen J.; Puntanen, Simo

Acta Comment. Univ. Tartu. Math. 14, 27-33 (2010).

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.)

Keywords:

best linear unbiased estimator; best linear unbiased predictor; generalized inverse; linear fixed effects model; orthogonal projector