The Annals of Statistics

Fiducial theory and optimal inference

Gunnar Taraldsen and Bo Henry Lindqvist

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 41, Number 1 (2013), 323-341.

Dates
First available in Project Euclid: 26 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1364302745

Digital Object Identifier
doi:10.1214/13-AOS1083

Mathematical Reviews number (MathSciNet)
MR3059420

Zentralblatt MATH identifier
1347.62019

Subjects
Primary: 62C05: General considerations
Secondary: 62A01: Foundations and philosophical topics 62F10: Point estimation 62F25: Tolerance and confidence regions 20N05: Loops, quasigroups [See also 05Bxx]

Keywords
Fiducial group model invariance risk frequentist inference

Citation

Taraldsen, Gunnar; Lindqvist, Bo Henry. Fiducial theory and optimal inference. Ann. Statist. 41 (2013), no. 1, 323--341. doi:10.1214/13-AOS1083. https://projecteuclid.org/euclid.aos/1364302745


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