On fiducial generators

Edilberto Nájera and Federico O’Reilly

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 5, 2232-2248

Abstract: Fiducial inference has been gaining presence recently and it is the intention of the present article to look at the notion of fiducial generators; meaning procedures to simulate parameter values that in some sense correspond to simulations from some implicit fiducial distribution. It is well known that when the distribution has group structure, stemming from the natural pivotal associated, a fiducial may be obtained. It is in the non group distributions that there appears to be still room for finding a fiducial distribution. Recently some general procedures have been proposed for dealing with generalized fiducials, but these depend on certain choices for a structural equation or a fiducial equation, as in Hannig (2009) or Taraldsen and Lindqvist (2013), respectively. A brief presentation is made of an earlier approach to fiducial inference for multivariate parameters, as in Brillinger (1962), and the implied fiducial generator introduced in Engen and Lillegård (1997), trying to connect them. Three interesting non group distributions are seen; two of them, the truncated exponential and the two-parameter gamma, already reported in literature. A third non group distribution is analyzed; the inverse Gaussian, connecting the fiducial that results following Brillinger (1962), with a result pertaining confidence limits for the shape parameter in Hsieh (1990). In the three cases, comparisons are made with the Bayesian posteriors that have been known to be close numerically. Some discussion is made on the issue of singularities of the fiducial density and its connection with densities that do not integrate to unity. As to the case of discrete observables, some comments are made for the Bernoulli distribution, only.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2015.1040505 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:46:y:2017:i:5:p:2232-2248

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2015.1040505

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().