Assume that a general linear random-effects model $y = Xbe + ve$ is given, and new observations in the future follow the linear model $y_{!f} = X_{!f}be + ve_{!f}$. This paper shows how to establish all possible best linear unbiased predictors (BLUPs) under the general linear random-effects model with original and new observations from the original observation vector $y$ under a most general assumption on the covariance matrix among the random vectors $be$, $ve$ and $ve_{!f}$. It utilizes a standard method of solving optimization problem in the L"owner partial ordering on a constrained quadratic matrix-valued function, and obtains analytical expressions of the BLUPs, including those for $y_{!f}$, $X_{!f}be$ and $ve_{!f}$. In particular, some fundamental equalities for the BLUPs are established under the linear random-effects model.
展开▼
