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Fiducial and Confidence Distributions for Real Exponential Families
Author(s) -
Veronese Piero,
Melilli Eugenio
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12117
Subject(s) - fiducial marker , mathematics , exponential family , confidence interval , bayesian probability , exponential distribution , distribution (mathematics) , prior probability , exponential function , bayesian inference , posterior predictive distribution , fiducial inference , statistics , calculus (dental) , bayesian statistics , mathematical analysis , bayesian linear regression , artificial intelligence , computer science , medicine , dentistry
We develop an easy and direct way to define and compute the fiducial distribution of a real parameter for both continuous and discrete exponential families. Furthermore, such a distribution satisfies the requirements to be considered a confidence distribution. Many examples are provided for models, which, although very simple, are widely used in applications. A characterization of the families for which the fiducial distribution coincides with a Bayesian posterior is given, and the strict connection with Jeffreys prior is shown. Asymptotic expansions of fiducial distributions are obtained without any further assumptions, and again, the relationship with the objective Bayesian analysis is pointed out. Finally, using the Edgeworth expansions, we compare the coverage of the fiducial intervals with that of other common intervals, proving the good behaviour of the former.