On decompositions of BLUEs under a partitioned linear model with restrictions

Zhang, Xuan; Tian, Yongge

doi:10.1007/s00362-014-0654-y

Cited by 14 publications

(5 citation statements)

References 19 publications

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“…Our main purpose is to derive various inequalities and equalities for comparison of covariance matrices of the BLUPs/BLUEs of all unknown vectors in the CPLM and its CRLMs. Previous and recent work on the problems of the inference of CPLMs can be found in; see e.g., [4]- [18] among others.…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models

Büyükkaya

Güler

2022

Fundamental Journal of Mathematics and Applications

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In this study, we consider a partitioned linear model with linear partial parameter constrains, known as a constrained partitioned linear model (CPLM), and its reduced models. A group of formulas on best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) in CPLM is derived via some quadratic matrix optimization methods, and further many basic properties of the predictors and estimators are established under some general assumptions. Our main purpose is to derive various inequalities and equalities for the comparison of covariance matrices of BLUPs and BLUEs under CPLM and its reduced models.

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Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models

Büyükkaya

Güler

2022

Fundamental Journal of Mathematics and Applications

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“…hold under (42) and (43), while the rank formulas in Theorems 6.2-6.6 reduce to certain simple and separated forms, as these given in [6]. When A 1 D 0; : : : ; A k D 0 in (1) and (2), Theorems 6.2-6.6 reduce to the results given in [5].…”

mentioning

confidence: 83%

“…in [11][12][13]. Some recent work on the MRM in the analysis of additive decompositions of BLUEs under linear models were presented in [4][5][6], while some contributions on MRM in the statistical analysis of CGLMs can be found in [14][15][16][17][18][19][20][21][22][23][24].…”

Section: Some Preliminaries In Linear Algebramentioning

confidence: 99%

“…The problem on additive decompositions of BLUEs under general liner models was approached in [4,5]. Zhang and Tian [6] recently investigated the above two decomposition identities for k D 2 by using some effective algebraic methods of dealing with additive decompositions of matrix expressions and ranks/ranges of matrices. Before proceeding, we introduce the notation to the reader and explain its usage in this paper.…”

Section: Introductionmentioning

confidence: 99%

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On decompositions of estimators under a general linear model with partial parameter restrictions

2017

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A general linear model can be given in certain multiple partitioned forms, and there exist submodels associated with the given full model. In this situation, we can make statistical inferences from the full model and submodels, respectively. It has been realized that there do exist links between inference results obtained from the full model and its submodels, and thus it would be of interest to establish certain links among estimators of parameter spaces under these models. In this approach the methodology of additive matrix decompositions plays an important role to obtain satisfactory conclusions. In this paper, we consider the problem of establishing additive decompositions of estimators in the context of a general linear model with partial parameter restrictions. We will demonstrate how to decompose best linear unbiased estimators (BLUEs) under the constrained general linear model (CGLM) as the sums of estimators under submodels with parameter restrictions by using a variety of effective tools in matrix analysis. The derivation of our main results is based on heavy algebraic operations of the given matrices and their generalized inverses in the CGLM, while the whole contributions illustrate various skillful uses of state-of-the-art matrix analysis techniques in the statistical inference of linear regression models.

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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: 98%

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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On decompositions of BLUEs under a partitioned linear model with restrictions

Cited by 14 publications

References 19 publications

On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models

On Predictors and Estimators under a Constrained Partitioned Linear Model and its Reduced Models

On decompositions of estimators under a general linear model with partial parameter restrictions

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

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