Some remarks on general linear model with new regressors

Lu, Changli; Gan, Shengjun; Tian, Yongge

doi:10.1016/j.spl.2014.10.015

Cited by 18 publications

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References 17 publications

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“…This paper introduced inertia and rank expansion formulas into the analysis of covariance matrices in statistical inferences, and established many new equalities and inequalities for covariance matrices of estimators via these inertia and rank formulas. Some recent work on this subject can be found in Dong et al (2014); Lu et al (2015); Tian (2015a, b); Tian and Zhang (2011);Zhang and Tian (2015).…”

Section: Rank/inertia Formulas For Olses' Covariance Matricesmentioning

confidence: 99%

Some equalities and inequalities for covariance matrices of estimators under linear model

Tian

2015

Stat Papers

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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.

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