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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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