A Bayesian variation of Basu's theorem and its ramification in statistical inference

One of the celebrated results of Professor D. Basu is his 1955 paper on ancillary statistics, which established the well known Basu’s Theorem. A Bayesian version of this result, where the parameter Θ is treated as a random variable, is developed in this note, along with other extensions of the related classical results, such as Rao-Blackwell and Lehmann-Scheffe theorems and the relation between complete sufficiency and minimal sufficiency. These extensions shed new lights on these fundamental theorems for frequentist statistical inference in the context Bayesian inference.

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s13171-023-00334-6

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Work Title A Bayesian variation of Basu's theorem and its ramification in statistical inference
Access
Open Access
Creators
  1. G. Jogesh Babu
  2. Bing Li
Keyword
  1. Rao-Blackwell theorem
  2. Lehmann-Scheffé theorem
  3. Complete sufficiency
  4. Minimal sufficiency
  5. Ancillary statistics
  6. Independence
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Sankhya A
Publication Date December 22, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/s13171-023-00334-6
Deposited March 05, 2024

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Version 1
published

  • Created
  • Added BayesianComplet-sufficiency-final.pdf
  • Added Creator G. Jogesh Babu
  • Added Creator Bing Li
  • Published
  • Updated Keyword, Publisher Show Changes
    Keyword
    • Rao-Blackwell theorem, Lehmann-Scheffé theorem, Complete sufficiency, Minimal sufficiency, Ancillary statistics, Independence
    Publisher
    • Sankhya A
    • Sankhya A
  • Updated