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Equality of BLUES or BLUPS under two linear models using stochastic restrictions. (English) Zbl 1247.62167
Summary: We consider mixed linear models, possibly with singular covariance matrices, by supplementing a particular fixed effects model with appropriate stochastic restrictions. We show that all representations of the best linear unbiased estimator (BLUE) and best linear unbiased predictor (BLUP) can be obtained through the augmented model including stochastic restrictions. Using this approach, we consider two mixed linear models, $$\mathcal M_{1}$$ and $$\mathcal M_{2}$$, say, which have different covariance matrices. We give necessary and sufficient conditions that the BLUP and/or BLUE under the the model $$\mathcal M_{1}$$ continue to be BLUP and/or BLUE also under the model $$\mathcal M_{2}$$.

##### MSC:
 62J05 Linear regression; mixed models 62F10 Point estimation 62F30 Parametric inference under constraints 15A09 Theory of matrix inversion and generalized inverses
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