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Some equalities and inequalities for covariance matrices of estimators under linear model. (English) Zbl 1365.62207
Summary: Best linear unbiased estimators (BLUEs) of unknown parameters under linear models have minimum covariance matrices in the Löwner partial ordering among all linear unbiased estimators of the unknown parameters. Hence, BLUEs’ covariance matrices are usually used as a criterion to compare optimality with other types of estimator. During this work, people often need to establish certain equalities and inequalities for BLUEs’ covariance matrices, and use them in statistical inference of regression models. This paper aims at establishing some analytical formulas for calculating ranks and inertias of BLUEs’ covariance matrices under general linear model, and using these formulas in the comparison of covariance matrices of BLUEs with other types of estimator. This is in fact a mathematical work, and some new tools in matrix analysis are essentially utilized.

##### MSC:
 62H12 Estimation in multivariate analysis 62J05 Linear regression; mixed models 62J10 Analysis of variance and covariance (ANOVA)
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