Some Asymptotic Results for Fiducial and Confidence Distributions

TL;DR

This paper derives simple, order O(1/n) accurate approximations for fiducial and confidence distributions under regularity conditions, exploring their asymptotic normality and connections with Bayesian posteriors.

Contribution

It introduces asymptotic approximations for fiducial and confidence distributions and analyzes their properties, including invariance and relation to Bayesian methods.

Findings

Fiducial distributions are asymptotically normal for the mean of exponential families.

Approximations are accurate to order O(1/n).

Fiducial distributions are invariant to component ordering.

Abstract

Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations are accurate at least to order O(1/n). For the mean parameter of a multivariate exponential family, our fiducial distribution is asymptotically normal and invariant to the importance ordering of the components of the mean parameter.