FIDUCIAL THEORY AND OPTIMAL INFERENCE

@article{Taraldsen2013FIDUCIALTA,
  title={FIDUCIAL THEORY AND OPTIMAL INFERENCE},
  author={Gunnar Taraldsen and Bo Henry Lindqvist},
  journal={Annals of Statistics},
  year={2013},
  volume={41},
  pages={323-341}
}
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… 
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References

SHOWING 1-10 OF 46 REFERENCES
ON GENERALIZED FIDUCIAL INFERENCE
In this paper we extend Fisher's fiducial argument and obtain a gener- alized fiducial recipe that greatly expands the applicability of fiducial ideas. We do this assuming as little structure as
Default priors for Bayesian and frequentist inference
Summary.  We investigate the choice of default priors for use with likelihood for Bayesian and frequentist inference. Such a prior is a density or relative density that weights an observed likelihood
The fiducial method and invariance
1930. In papers since that time Fisher has frequently discussed aspects of the method and may have, in the view of some readers. modified or altered his ideas concerning the underlying principles and
Improper Priors Are Not Improper
It is well known that improper priors in Bayesian statistics may lead to proper posterior distributions and useful inference procedures. This motivates us to give an elementary introduction to a
Generalized fiducial inference via discretization
TLDR
In this paper, theoretical properties of generalized fiducial distribution introduced in Hannig (2009) for discretized data are investigated and limit theorems are provided for both fixed sample size with increasing precision of the discretization, and increasing sample sizes with fixed Precision.
Fiducial limits of the parameter of a discontinuous distribution.
TLDR
This chapter discusses methods of interval estimation which can be used successfully in the case of continuous distributions but encounter a special kind of difficulty when they are applied to a discontinuous distribution such as the binomial or the Poisson.
Statistical inference: fiducial and structural vs. likelihood
The mathematical model assumptions, justifying fiducial, structural or likelihood inferences, are discussed. In this connection is clarified, that the known paradoxes with fiducial or structural can
Dempster-Shafer Theory and Statistical Inference with Weak Beliefs
TLDR
A general description of WB in the context of inferential models, its interplay with the DS calculus, and the maximal belief solution is presented, and new applications of the WB method in two high-dimensional hypothesis testing problems are given.
Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model
In this article we propose a new method for constructing confidence intervals for σα2,σϵ2, and the intraclass correlation ρ==σα2(σα2++σε2) in a two-component mixed-effects linear model. This method
Pivotal methods in the propagation of distributions
We propose a method for assigning a probability distribution to an input quantity. The distribution is used in a Monte Carlo method described in Supplement 1 to the Guide to the Expression of
...
1
2
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4
5
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