Some Remarks on BLUP under the General Linear Model with Linear Equality Restrictions

Abstract:

      In this paper, we give the representation of the best linear unbiased predictor (BLUP) of the new observations under $\mathscr{M}_{r_{f}}$. Through the representation, we give necessary and sufficient conditions that the estimators, OLSEs (ordinary least squares estimators) and BLUEs (best linear unbiased estimators), under $\mathscr{M}_{f}$ and $\mathscr{M}_{r_{f}},$ and the predictor, BLUP, under $\mathscr{M}_{f}$ continue to be the BLUP under $\mathscr{M}_{r_{f}}$, respectively.