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Comparing the BLUEs under two linear models. (English) Zbl 1319.62138
Summary: In this article, we consider two linear models, \(\mathcal{M}_1=\{y, X\beta, V_1\}\) and \(\mathcal{M}_2=\{y, X\beta, V_2\}\), which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of \(X\beta\) under these models. The corresponding problems between the models \(\{y, X\beta, I_n\}\) and \(\{y, X\beta, V\}\), i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of \(X\beta\) under \(\mathcal{M}_1\) and \(\mathcal{M}_2\). This article is an expository one presenting also new results.

MSC:
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
62H20 Measures of association (correlation, canonical correlation, etc.)
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