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A new derivation of BLUPs under random-effects model. (English) Zbl 1329.62264
Summary: This paper considers predictions of vectors of parameters under a general linear model $$y= X\beta + \varepsilon$$ with the random coefficients $$\beta$$ satisfying $$\beta = A\alpha + \gamma$$. It utilizes a standard method of solving constrained quadratic matrix-valued function optimization problem in the Löwner partial ordering, and obtains the best linear unbiased predictor (BLUP) of given vector $$F\alpha + G\gamma + H\varepsilon$$ of the unknown parameters in the model. Some special cases of the BLUPs are also presented. In particular, a general decomposition equality $$y = \text{BLUE}(XA\alpha) + \text{BLUP}(X\gamma) + \text{BLUP}(\varepsilon)$$ is proved under the random-effects model. A further problem on BLUPs of new observations under the random-effects model is also addressed.

##### MSC:
 62H12 Estimation in multivariate analysis 62J05 Linear regression; mixed models 62J10 Analysis of variance and covariance (ANOVA)
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