Open Access
VOL. 54 | 2007 Confidence distribution (CD) -- distribution estimator of a parameter
Kesar Singh, Minge Xie, William E. Strawderman

Editor(s) Regina Liu, William Strawderman, Cun-Hui Zhang

IMS Lecture Notes Monogr. Ser., 2007: 132-150 (2007) DOI: 10.1214/074921707000000102


The notion of confidence distribution (CD), an entirely frequentist concept, is in essence a Neymanian interpretation of Fisher's Fiducial distribution. It contains information related to every kind of frequentist inference. In this article, a CD is viewed as a distribution estimator of a parameter. This leads naturally to consideration of the information contained in CD, comparison of CDs and optimal CDs, and connection of the CD concept to the (profile) likelihood function. A formal development of a multiparameter CD is also presented.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

MathSciNet: MR2459184

Digital Object Identifier: 10.1214/074921707000000102

Primary: 62F03 , 62F12 , 62G05
Secondary: 62G10 , 62G20

Keywords: bootstrap , confidence distribution , data-depth , Fiducial inference , frequentist inference , likelihood function , optimality , p-value functio

Rights: Copyright © 2007, Institute of Mathematical Statistics

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