Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models
文献类型：期刊论文
| 作者 | Wu, QG; Yang, GQ |
| 刊名 | SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
 |
| 出版日期 | 2002-07-01 |
| 卷号 | 45期号:7页码:845-858 |
| 关键词 | uniformly minimum risk equivariant estimator affine group of transformations quadratic loss matrix loss |
| ISSN号 | 1006-9283 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000176851400004 |
| 出版者 | SCIENCE CHINA PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/16968]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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