KMS Of Academy of mathematics and systems sciences, CAS
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 Publication | SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY |
ISSN | 1006-9283 |
Volume | 45Issue:7Pages:845-858 |
Abstract | 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. |
Keyword | uniformly minimum risk equivariant estimator affine group of transformations quadratic loss matrix loss |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000176851400004 |
Publisher | SCIENCE CHINA PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/16969 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Wu, QG |
Affiliation | Chinese 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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