Empirical BLUE and BLUP

Dale L. Zimmerman
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Dale L. Zimmerman: University of Iowa, Department of Statistics and Actuarial Science

Chapter 17 in Linear Model Theory, 2020, pp 487-497 from Springer

Abstract: 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 y u , X β 0 , V y y ( θ ) v y u ( θ ) v y u ( θ ) T v u u ( θ ) , $$\displaystyle \left \{\left (\begin {array}{c}\mathbf {y} \\ u\end {array}\right ),\left (\begin {array}{c}\mathbf { X}\boldsymbol {\beta } \\ 0 \end {array}\right ),\left (\begin {array}{cc}{\mathbf {V}}_{yy}(\boldsymbol {\theta }) & {\mathbf {v}}_{yu}(\boldsymbol {\theta }) \\ {\mathbf {v}}_{yu}(\boldsymbol {\theta })^T & \mathbf { v}_{uu}(\boldsymbol {\theta }) \end {array}\right )\right \}, $$ is to first obtain an estimate θ ̂ $$\hat {\boldsymbol {\theta }}$$ of θ and then proceed as though this estimate was the true θ.

Date: 2020
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DOI: 10.1007/978-3-030-52063-2_17

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