Summary
Pre-experimental Frequentist error probabilities do not summarize adequately the strength of evidence from data. The Conditional Frequentist paradigm overcomes this problem by selecting a “neutral” statistic S to reflect the strength of the evidence and reporting a conditional error probability, given the observed value of S. We introduce a neutral statistic S that makes the Conditional Frequentist error reports identical to Bayesian posterior probabilities of the hypotheses. In symmetrical cases we can show this strategy to be optimal from the Frequentist perspective. A Conditional Frequentist who uses such a strategy can exploit the consistency of the method with the Likelihood Principle — for example, the validity of sequential hypothesis tests even if the stopping rule is informative or is incompletely specified.
Research supported by United States National Science Foundation grant DMS-9305699 and Environmental Protection Agency grant CR822047-01-0, and performed in collaboration with James O. Berger and Lawrence D. Brown.
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References
Berger, J.O. (1985): Statistical Decision Theory and Bayesian Analysis ( 2nd edn. ). Springer-Verlag, New York.
Berger, J.O., Brown, L.D., and Wolpert, R.L. (1994): A unified conditional frequentist and Bayesian test for fixed and sequential simple hypothesis testing. Ann. Statist 22, 1787–1807.
Berger, J.O., and Wolpert, R.L. (1988): The Likelihood Principle: Review, Generalizations, and Statistical Implications (2nd edn.) (with Discussion). Institute of Mathematical Statistics Press, Hayward, CA.
Brown, L.D. (1978): A contribution to Kiefer’s theory of conditional confidence procedures. Ann. Statist. 6, 59–71.
Brownie, C., and Kiefer, J. (1977): The ideas of conditional confidence in the simplest setting. Comniun. Statist.–Theory Meth. A6 (8), 691–751.
Kiefer, J. (1975): Conditional confidence approach in multi-decision problems. In: P.R. Krishnaiah (ed.): Multivariate Analysis I V. Academic Press, New York.
Kiefer, J. (1977): Conditional confidence statements and confidence estimators (with discussion). J. Amer. Statist. Assoc. 72, 789–827.
Lehmann, E.L. (1986): Testing statistical hypotheses (2nd edn.). John Wiley k Sons, New York; reprinted 1994 by Chapman k Hall, New York.
Siegmund, D. (1985): Sequential Analysis: Tests and Confidence Intervals. Springer–Verlag, New York.
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© 1996 Springer-Verlag Berlin · Heidelberg
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Wolpert, R.L. (1996). Testing Simple Hypotheses. In: Bock, HH., Polasek, W. (eds) Data Analysis and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80098-6_24
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DOI: https://doi.org/10.1007/978-3-642-80098-6_24
Publisher Name: Springer, Berlin, Heidelberg
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