A new derivation of BLUPs under random-effects model

Yongge Tian ()

Metrika: International Journal for Theoretical and Applied Statistics, 2015, vol. 78, issue 8, 905-918

Abstract: This paper considers predictions of vectors of parameters under a general linear model $$\mathbf{y}= \mathbf{X}{\pmb {\beta }}+ {\pmb {\varepsilon }}$$ y = X β + ε with the random coefficients $${\pmb {\beta }}$$ β satisfying $${\pmb {\beta }}=\mathbf{A}{\pmb {\alpha }}+ {\pmb {\gamma }}$$ β = A α + γ . 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 $$\mathbf{F}{\pmb {\alpha }}+ \mathbf{G}\varvec{\gamma } + \mathbf{H}{\pmb {\varepsilon }}$$ F α + G γ + H ε of the unknown parameters in the model. Some special cases of the BLUPs are also presented. In particular, a general decomposition equality $$\mathbf{y}= \mathrm{BLUE}(\mathbf{X}\mathbf{A}{\pmb {\alpha }}) + \mathrm{BLUP}(\mathbf{X}{\pmb {\gamma }}) + \mathrm{BLUP}({\pmb {\varepsilon }})$$ y = BLUE ( X A α ) + BLUP ( X γ ) + BLUP ( ε ) is proved under the random-effects model. A further problem on BLUPs of new observations under the random-effects model is also addressed. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Linear model; Random effects; Quadratic matrix-valued function; BLUP; Covariance matrix; 62H12; 62J05; 62J10 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s00184-015-0533-0

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