Abstract

It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof does not rely on existence of invariant measures, and generalizes results corresponding to the choice of the right Haar measure as a Bayesian prior. Classical and more recent examples show that fiducial arguments can be used to give good candidates for exact or approximate confidence distributions. It is here suggested that the fiducial algorithm can be considered as an alternative to the Bayesian algorithm for the construction of good frequentist inference procedures more generally.

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Gunnar Taraldsen. Bo Henry Lindqvist. "Fiducial theory and optimal inference." Ann. Statist. 41 (1) 323 - 341, February 2013. https://doi.org/10.1214/13-AOS1083

Information

Published: February 2013

First available in Project Euclid: 26 March 2013

Digital Object Identifier: 10.1214/13-AOS1083

Subjects:

Primary: 62C05

Secondary: 20N05 , 62A01 , 62F10 , 62F25

Keywords: Fiducial , frequentist inference , group model , Invariance , risk

JOURNAL ARTICLE
19 PAGES

Vol.41 • No. 1 • February 2013

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