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Fiducial inference in the pivotal family of distributions

文献类型：期刊论文

作者Xu, XZ; Li, GY
刊名SCIENCE IN CHINA SERIES A-MATHEMATICS
出版日期2006-03-01
卷号49期号:3页码:410-432
关键词confidence bounds fiducial distributions fiducial model frequentist property generalized pivotal model pivotal family of distributions testing hypotheses
ISSN号1006-9283
DOI10.1007/s11425-006-0410-4
英文摘要In this paper a family, called the pivotal family, of distributions is considered. A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given. The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000236874200010
出版者SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/3182]  
专题中国科学院数学与系统科学研究院
通讯作者Xu, XZ
作者单位1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式
GB/T 7714		 Xu, XZ,Li, GY. Fiducial inference in the pivotal family of distributions[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS,2006,49(3):410-432.
APA Xu, XZ,&Li, GY.(2006).Fiducial inference in the pivotal family of distributions.SCIENCE IN CHINA SERIES A-MATHEMATICS,49(3),410-432.
MLA Xu, XZ,et al."Fiducial inference in the pivotal family of distributions".SCIENCE IN CHINA SERIES A-MATHEMATICS 49.3(2006):410-432.

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来源：数学与系统科学研究院

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