Advertisement

Fiducial Inference

  • Robert Buehler
Part of the Lecture Notes in Statistics book series (LNS, volume 1)

Abstract

The concept of fiducial probability is due to R.A. Fisher. The fiducial distribution of a parameter θ given an observation x is intended to describe our uncertainty about θ after x is observed when there was no a priori information about θ. The term “fiducial distribution” first appeared in Fisher’s 1930 paper [CP 84], where the distribution of the correlation coefficient was considered. Unfortunately, Fisher never gave an acceptable general definition of fiducial probability.

Keywords

Royal Statistical Society Ancillary Statistic Simultaneous Distribution Fiducial Probability Fiducial Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anscombe, F.J. (1957). “Dependence of the Fiducial Argument on the Sampling Rule,” Biometrika, 44, 464–469.MathSciNetzbMATHGoogle Scholar
  2. Behrens, W.-V. (1929). “Ein Betrag zur Fehlenberechnung bei wenigen Beobachtungen,” Landwirtschaftliche Jahrbucher, 68, 807–837.Google Scholar
  3. Buehler, R.J. and A.. P. Feddersen (1963). “Note on a Conditional Property of Student’s t,” The Annals of Mathematical Statistics, 34, 1098–1100.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Brillinger, D.R. (1962). “Examples of the Definition of Fiducial Probability with a Bibliography,” The Annals of Mathematical Statistics, 33, 1349–1355.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Creasy, M.A. (1954). “Limits for the Ratio of Me ins,” Journal of the Royal Statistical Society, Series B, 16, 186–194.MathSciNetzbMATHGoogle Scholar
  6. Fieller, E.C. (. 1954 ), “Some Problems in Interval Estimation,” Journal of the Royal Statistical Society, Series B, 16, 175–185.MathSciNetzbMATHGoogle Scholar
  7. Fraser, D.A.S. (1968). The Structure of Inference. New York: John Wiley and Sons.zbMATHGoogle Scholar
  8. Lindley, D.V. (1958). “Fiducial Distributions and Bayes’ Theorem,” Journal of the Royal Statistical Society, Series B, 20, 102–107.MathSciNetzbMATHGoogle Scholar
  9. Pitman, E.J.G. (1939). “The Estimation of the Location and Scale Parameters of a Continuous Population of any Given Form,” Biometrika, 30, 391–421.zbMATHGoogle Scholar
  10. Tukey, J.W. (1957). “Some Examples with Fiducial Relevance,” The Annals of Mathematical Statistics, 28, 687–695.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Wilkinson, G.N. (1977). “On Resolving the Controversy in Statistical Inference,” Journal of the Royal Statistical Society, Series B, 39, 119–171.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Robert Buehler

There are no affiliations available

Personalised recommendations