Some decompositions of OLSEs and BLUEs under a partitioned linear model

doi:10.1111/j.1751-5823.2007.00018.x

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	Some decompositions of OLSEs and BLUEs under a partitioned linear model
	Tian, Yongge
刊名	INTERNATIONAL STATISTICAL REVIEW
	2007-08
卷号	75 期号:2 页码:224-248
关键词	partitioned linear model small model ordinary least squares estimator (OLSE) best linear unbiased estimator (BLUE) decomposition of estimator rank formulas for partitioned matrices elementary block matrix operations (EBMOs)
ISSN号	0306-7734
DOI	10.1111/j.1751-5823.2007.00018.x
英文摘要	We consider in this paper a partitioned linear model {y, X-1 beta(1) + X-2 beta(2), sigma(2)Sigma} and two corresponding small models {y, X-1 beta(1), sigma(2)Sigma} and {y, X-2 beta(2), sigma(2)Sigma}. We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full model to be the sum of the ordinary least squares estimators under the two small models; (ii) the best linear unbiased estimator under the full model to be the sum of the best linear unbiased estimators under the two small models; (iii) the best linear unbiased estimator under the full model to be the sum of the ordinary least squares estimators under the two small models. The proofs of the main results in this paper also demonstrate how to use the matrix rank method for characterizing various equalities of estimators under general linear models.
WOS研究方向	Mathematics
语种	英语
出版者	INT STATISTICAL INST
WOS记录号	WOS:000249135700008
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2588]
专题	上海财经大学
通讯作者	Tian, Yongge
作者单位	Shanghai Univ Finance & Econ, Sch Econ, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Tian, Yongge. Some decompositions of OLSEs and BLUEs under a partitioned linear model[J]. INTERNATIONAL STATISTICAL REVIEW,2007,75(2):224-248.
APA	Tian, Yongge.(2007).Some decompositions of OLSEs and BLUEs under a partitioned linear model.INTERNATIONAL STATISTICAL REVIEW,75(2),224-248.
MLA	Tian, Yongge."Some decompositions of OLSEs and BLUEs under a partitioned linear model".INTERNATIONAL STATISTICAL REVIEW 75.2(2007):224-248.