On properties of BLUEs under general linear regression models

Tian, Yongge

doi:10.1016/j.jspi.2012.10.005

Cited by 22 publications

(8 citation statements)

References 37 publications

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“…According to Rao [1], the problem of inference from a linear model can be completely solved when one has obtained an arbitrary generalized inverse of the partitioned matrix Z . This approach based on the numerical evaluation of an inverse of the partitioned matrix Z is known as the IPM method, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section:  mentioning

confidence: 99%

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IPM yöntemi ile alt parametrelerin tahmini

Eriş¹,

Güler

2016

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In this study, a general partitioned linear modelis considered to determine the best linear unbiased estimators (BLUEs) of subparameters 1 1 X  and 2 2 X  . Some results are given related to the BLUEs of subparameters by using the inverse partitioned matrix (IPM) method based on a generalized inverse of a symmetric block partitioned matrix which is obtained from the fundamental BLUE equation.

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Section:  mentioning

confidence: 99%

“…Some valuable properties of BLUE have been obtained, e.g., [2][3][4][5][6]. By applying matrix rank method, some characterizations of BLUE have been given by Tian [7,8]. IPM method for the general linear model with linear restrictions has been considered by Baksalary [9].…”

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confidence: 99%

IPM yöntemi ile alt parametrelerin tahmini

Eriş¹,

Güler

2016

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“…More results on algebraic properties of P K;X; and P X; in (2.23) and (2.24) were given in Isotalo et al (2008); Tian (2013).…”

Section: Lemma 4 Letmentioning

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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“…A huge amount of new expansion formulas, like those in Lemmas 2.4 and 2.5, for calculating ranks of matrices were established in the past several decades. These formulas are so ground-breaking in both theory and applications that people can employ them in simplifying various complicated matrix expressions or equalities occurring in statistics, while the results obtained can easily be represented as some simple rank equalities, range equalities or matrix equations; see, e.g., Tian (2007Tian ( , 2009Tian ( , 2010Tian ( , 2012Tian ( , 2013, Tian and Takane (2008) and Tian and Zhang (2011). In this note, we also use the matrix rank method to characterize relations between BLUEs of parametric functions under (1.1) and (1.2).…”

Section: This Matrix Equation Is Consistent As Well If Xa = B Is Consmentioning

confidence: 99%