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

• Autorzy: Bo Jiang , Yongge Tian , Xuan Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Partitioned linear model; Submodel; Parameter restriction; BLUE; Additive matrix decomposition

Kategorie tematyczne

• 15A09: Matrix inversion, generalized inverses
• 62F30: Inference under constraints
• 15A03: Vector spaces, linear dependence, rank
• 62F10: Point estimation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1300-1322

Daty

wydano

2017-01-01

otrzymano

2017-02-23

zaakceptowano

2017-09-26

online

2017-12-02

Twórcy

autor

Bo Jiang

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autor

Yongge Tian

• , , ,

autor

Xuan Zhang

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Identyfikatory

DOI

10.1515/math-2017-0109