Fiducial inference in the pivotal family of distributions

doi:10.1007/s11425-006-0410-4

	Fiducial inference in the pivotal family of distributions
	Xu, XZ ; Li, GY
刊名	SCIENCE IN CHINA SERIES A-MATHEMATICS
	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
DOI	10.1007/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
出版者	SCIENCE PRESS
WOS记录号	WOS:000236874200010
内容类型	期刊论文
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.