Abstract
Fiducial inference introduced the pivotal inversion that is central to modern confidence theory. Initially this provided confidence bounds but later was generalized to give confidence distributions on the paramseter space. For this it came in direct conflict with the then prominent Bayesian approach called inverse probability. Confidence distributions are now however widespread in modern likelihood theory. Recent results from this theory indicate that the developed fiducial confidence approach is giving a consistent statement of where the parameter is with respect to the data, and indeed is consistent with recent Bayesian approaches that allow data dependent priors.
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Bibliography
Bayes, T. 1763. An essay towards solving a problem in the doctrine of chance. Philosophical Transactions of the Royal Society of London 53: 370–418 .Reprinted in Biometrika 45 (1958), 293–315
Dawid, A., M. Stone, and J. Zidek. 1973. Marginalization paradoxes in Bayesian and structural inference. Journal of the Royal Statistical Society B 35: 189–233.
Fisher, R. 1922. On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society A 222: 309–368.
Fisher, R. 1930. Inverse probability. Proceedings of the Cambridge Philosophical Society 26: 528–535.
Fisher, R. 1933. The concept of inverse probability and fiducial probability referring to unknown parameters. Proceedings of the Royal Statistical Society A 139: 343–348.
Fisher, R. 1935. The fiducial argument in statistical inference. Annals of Eugenics 6: 391–398.
Fisher, R. 1956. Statistical methods and scientific inference. Edinburgh: Oliver and Boyd.
Fraser, D. 1961. The fiducial method and invariance. Biometrika 48: 261–280.
Fraser, D. 1995. Some remarks on pivotal models and the fiducial arguments in relation to structural models. International Statistical Review 64: 231–236.
Fraser, D. 2004. Ancillaries and conditional inference, with discussion. Statistical Science 19: 333–369.
Fraser, D., and N. Reid. 2001. Ancillary information for statistical inference. In Empirical Bayes and likelihood inference, ed. S. Ahmed and N. Reid. New York: Springer-Verlag.
Fraser, D., and N. Reid. 2002. Strong matching of frequentist and Bayesian inference. Journal of Statistical Planning and Inference 103: 263–285.
Fraser, D., N. Reid, and J. Wu. 1999. A simple general formula for tail probabilities for frequentist and Bayesian inference. Biometrika 86: 249–264.
Lindley, D. 1958. Fiducial distribution and Bayes’ theorem. Journal of the Royal Statistical Society B 20: 102–107.
Neyman, J. 1941. Fiducial argument and the theory of confidence intervals. Biometrika 32: 128–150.
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Fraser, D.A.S. (2018). Fiducial Inference. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2008
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2008
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