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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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