A Bayesian Variation of Basu’s Theorem and its Ramification in Statistical Inference

G. Jogesh Babu () and Bing Li ()
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G. Jogesh Babu: The Pennsylvania State University
Bing Li: The Pennsylvania State University

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 7, 125-133

Abstract: Abstract 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 $$\Theta $$ 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-Scheffé theorems and the relation between complete sufficiency and minimal sufficiency. These extensions shed new light on these fundamental theorems for frequentist statistical inference in the context Bayesian inference.

Keywords: Rao-Blackwell theorem; Lehmann-Scheffé theorem; Complete sufficiency; Minimal sufficiency; Ancillary statistics; Independence; Primary 62F10; 62C10 Secondary 62F15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-023-00334-6

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