On Probability Matching Fiducial Distributions

• Activity Number: 503
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Abhishek Pal Majumder*+ and Jan Hannig
• Companies: University of North Carolina at Chapel Hill and University of North Carolina at Chapel Hill
• Keywords: Posterior quantile ; Fiducial inference ; Generalized inference ; Shrinkage argument ; Higher order asymptotics ; Jeffrey's prior

Abstract

Probability matching prior is one way to justify the superiority of Jeffrey's prior since the asymptotic coverage of its posterior quantile is first order exact. In this work we comparatively analyzed the conditions on the density function for which the Fiducial distribution will be first order exact and in cases we are able to generate that through a discreet choice of statistics. The study of generalized Fiducial inference has its own merit from the classical point of view since the ``priori" information of the parameter $\theta$ is driven by the structural data generating equation. In a way this work bridges and analyze two paradigms on a common ground of probability matching point of view and raises some important questions on the validity of the first order exact Fiducial distributions when some smoothness conditions of the density functions are violated.