Some Remarks on BLUP under the General Linear Model with Linear Equality Restrictions
Received:September 29, 2017  Revised:March 22, 2018
Key Word: general linear model   restricted linear model   BLUP   OLSE   BLUE  
Fund ProjectL:Supported by the Talent Program of Anhui Science and Technology University (Grant No.XXYJ201703).
Author NameAffiliation
Xingwei REN Department of Mathematics, Anhui Science and Technology University, Anhui 233100, P. R. China 
Leyi LIN Wentian College, Hohai University, Anhui 243031, P. R. China 
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      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.
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