Empirical BLUE and BLUP

Abstract

Recall from Sect. 13.5 that E-BLUP, the conventional procedure for predicting a predictable linear function τ = c ^Tβ + u under the prediction-extended general mixed linear model

$$\displaystyle \left \{\left (\begin {array}{c}\mathbf {y} \\ u\end {array}\right ),\left (\begin {array}{c}\mathbf { X}\boldsymbol {\beta } \\ 0 \end {array}\right ),\left (\begin {array}{cc}{\mathbf {V}}_{yy}(\boldsymbol {\theta }) & {\mathbf {v}}_{yu}(\boldsymbol {\theta }) \\ {\mathbf {v}}_{yu}(\boldsymbol {\theta })^T & \mathbf { v}_{uu}(\boldsymbol {\theta }) \end {array}\right )\right \}, $$

is to first obtain an estimate $\hat {\boldsymbol {\theta }}$ of θ and then proceed as though this estimate was the true θ.