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Fiducial Inference

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International Encyclopedia of Statistical Science

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Introduction

The origin of Generalized Fiducial Inference can be traced back to R. A. Fisher (Fisher 1930, 1933, 1935) who introduced the concept of a fiducial distribution for a parameter, and proposed the use of this fiducial distribution, in place of the Bayesian posterior distribution, for interval estimation of this parameter. In the case of a one-parameter family of distributions, Fisher gave the following definition for a fiducial density f(θ | x) of the parameter based on a single observation x for the case where the cdf F(x | θ) is a monotonic decreasing function of θ:

$$f(\theta /x) = -\frac{\partial F(x\vert \theta )} {\partial \theta } .$$

In simple situations, especially in one parameter families of distributions, Fisher’s fiducial intervals turned out to coincide with classical confidence intervals. For multiparameter families of distributions, the fiducial approach led to confidence sets whose frequentist coverage probabilities were close to the claimed confidence...

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Author information

Authors and Affiliations

  1. The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Jan Hannig (Associate Professor)

  2. Colorado State University, Fort Collins, CO, USA

    Hari Iyer (Professor)

  3. The University of California at Davis, Davis, CA, USA

    Thomas C. M. Lee (Professor)

Authors
  1. Jan Hannig
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  2. Hari Iyer
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  3. Thomas C. M. Lee
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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© 2011 Springer-Verlag Berlin Heidelberg

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Hannig, J., Iyer, H., Lee, T.C. (2011). Fiducial Inference. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_250

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