The Annals of Statistics

Fiducial theory and optimal inference

Gunnar Taraldsen and Bo Henry Lindqvist

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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

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

First available in Project Euclid: 26 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Fiducial group model invariance risk frequentist inference


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

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