Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

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	Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models
	Wu, QG; Yang, GQ
	2002-07-01
发表期刊	SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
ISSN	1006-9283
卷号	45 期号:7 页码:845-858
摘要	In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrix V and (trV)(alpha), where alpha > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators of V and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.
关键词	uniformly minimum risk equivariant estimator affine group of transformations quadratic loss matrix loss
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000176851400004
出版者	SCIENCE CHINA PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16969
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, QG
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wu, QG,Yang, GQ. Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,2002,45(7):845-858.
APA	Wu, QG,&Yang, GQ.(2002).Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models.SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,45(7),845-858.
MLA	Wu, QG,et al."Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models".SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY 45.7(2002):845-858.