Institute of Mathematical Statistics Lecture Notes - Monograph Series

Confidence distribution (CD) -- distribution estimator of a parameter

Kesar Singh, Minge Xie, and William E. Strawderman

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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.

Chapter information

Regina Liu, William Strawderman and Cun-Hui Zhang, eds., Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 132-150

First available in Project Euclid: 4 December 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 62F03: Hypothesis testing 62F12: Asymptotic properties of estimators 62G05: Estimation
Secondary: 62G10: Hypothesis testing 62G20: Asymptotic properties

confidence distribution frequentist inference fiducial inference optimality bootstrap data-depth likelihood function p-value functio

Copyright © 2007, Institute of Mathematical Statistics


Singh, Kesar; Xie, Minge; Strawderman, William E. Confidence distribution (CD) -- distribution estimator of a parameter. Complex Datasets and Inverse Problems, 132--150, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000102.

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