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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
Source PublicationSCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
ISSN1006-9283
Volume45Issue:7Pages:845-858
AbstractIn 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.
Keyworduniformly minimum risk equivariant estimator affine group of transformations quadratic loss matrix loss
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000176851400004
PublisherSCIENCE CHINA PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/16969
Collection中国科学院数学与系统科学研究院
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
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.
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