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Characterizations of the best linear unbiased estimator in the general Gauss-Markov model with the use of matrix partial orderings. (English) Zbl 0695.62152
Summary: Under the general Gauss-Markov model $$\{Y,X\beta,\sigma^ 2V\}$$, two new characterizations of BLUE(X,$$\beta)$$ are derived involving the Löwner and rank-subtractivity partial orderings between the dispersion matrix of BLUE(X$$\beta)$$ and the dispersion matrix of Y. As particular cases of these characterizations, three new criteria for the equality between OLSE(X$$\beta)$$ and BLUE(X$$\beta)$$ are given.

##### MSC:
 62J05 Linear regression; mixed models 06F99 Ordered structures
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##### References:
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