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

TL;DR

This paper explores confidence distributions as a frequentist distribution estimator of parameters, analyzing their information content, optimal forms, and connections to likelihood functions, including extensions to multiple parameters.

Contribution

It introduces a formal framework for confidence distributions as distribution estimators, compares different CDs, and extends the concept to multiparameter cases.

Findings

Confidence distributions contain comprehensive inference information.

Optimal confidence distributions can be characterized and compared.

The concept is extended to multiparameter settings.

Abstract

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.