Bernoulli

  • Bernoulli
  • Volume 5, Number 5 (1999), 833-854.

Consistency and strong inconsistency of group-invariant predictive inferences

Morris L. Eaton and William D. Sudderth

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Abstract

Consider a statistical model which is invariant under a group of transformations that acts transitively on the parameter space. In this situation, the problem of constructing invariant predictive distributions is considered. It is shown, under certain assumptions, that Fisherian pivoting and the use of right Haar measure as an improper prior distribution both yield the same invariant predictive distribution. Furthermore, it is shown that any other invariant predictive distribution is strongly inconsistent in the sense of Stone.

Article information

Source
Bernoulli, Volume 5, Number 5 (1999), 833-854.

Dates
First available in Project Euclid: 12 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1171290401

Mathematical Reviews number (MathSciNet)
MR1715441

Zentralblatt MATH identifier
0983.62004

Keywords
Fisherian pivoting improper prior distributions invariant predictive distribution proper action right Haar measure strong inconsistency

Citation

Eaton, Morris L.; Sudderth, William D. Consistency and strong inconsistency of group-invariant predictive inferences. Bernoulli 5 (1999), no. 5, 833--854. https://projecteuclid.org/euclid.bj/1171290401


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