Missouri Journal of Mathematical Sciences

Extending Edwards Likelihood Ratios to Simple One Sided Hypothesis Tests

Dewayne Derryberry and Milan Bimali

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Abstract

With regard to the one sided hypothesis test, we propose a likelihood ratio that might be viewed as a Bayes/Non-Bayes compromise in the spirit of I. J. Good (1983). The influence of A. W. F. Edwards (1972) will also be apparent. Although we will develop some general ideas, most of our effort will focus on tests of a single unknown mean and the specific case of a sample from a normal population with unknown mean and known variance.

Article information

Source
Missouri J. Math. Sci., Volume 26, Issue 1 (2014), 57-63.

Dates
First available in Project Euclid: 10 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1404997109

Digital Object Identifier
doi:10.35834/mjms/1404997109

Mathematical Reviews number (MathSciNet)
MR3263542

Zentralblatt MATH identifier
1306.62061

Subjects
Primary: 62A01: Foundations and philosophical topics

Keywords
Bayes factor inverse probability weight of evidence

Citation

Derryberry, Dewayne; Bimali, Milan. Extending Edwards Likelihood Ratios to Simple One Sided Hypothesis Tests. Missouri J. Math. Sci. 26 (2014), no. 1, 57--63. doi:10.35834/mjms/1404997109. https://projecteuclid.org/euclid.mjms/1404997109


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References

  • G. Casella and R. Berger, Reconciling Bayesian and frequentist evidence in the one-sided testing problem, Journal of the American Statistical Association, 82.397 (1987), 106–111.
  • R. Christensen, Testing, Fisher, Neyman, Pearson, and Bayes, The American Statistician, 59.2 (2005), 121–126.
  • M. H. DeGroot and M. J. Schervish, Probability and Statistics, 3rd ed., Addison-Wesley, 2002.
  • A. W. F. Edwards, Likelihood, Cambridge University Press, Cambridge (expanded edition, 1992, Johns Hopkins University Press, Baltimore), 1972.
  • I. J. Good, Good Reasoning: The Foundations of Probability and Its Applications, University of Minnesota Press, 1983.
  • I. J. Good, The Bayes/non-Bayes compromise: a brief review, Journal of the American Statistical Association, 87.419 (1992), 576–606.
  • R. E. Kass and A. E. Raftery, Bayes factors, Journal of the American Statistical Association, 90.430 (1995), 791.
  • F. L. Ramsey and D. W. Schafer, The Statistical Sleuth, Brooks/Cole, 1953.
  • P. R. Rosenbaum, Observational Studies, 2nd ed., Springer, New York, 2002.