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February 2019 Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters
David R. Bickel, Alexandre G. Patriota
Bernoulli 25(1): 47-74 (February 2019). DOI: 10.3150/17-BEJ942


Frequentist methods, without the coherence guarantees of fully Bayesian methods, are known to yield self-contradictory inferences in certain settings. The framework introduced in this paper provides a simple adjustment to $p$ values and confidence sets to ensure the mutual consistency of all inferences without sacrificing frequentist validity. Based on a definition of the compatibility of a composite hypothesis with the observed data given any parameter restriction and on the requirement of self-consistency, the adjustment leads to the possibility and necessity measures of possibility theory rather than to the posterior probability distributions of Bayesian and fiducial inference.


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David R. Bickel. Alexandre G. Patriota. "Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters." Bernoulli 25 (1) 47 - 74, February 2019.


Received: 1 December 2014; Revised: 1 March 2017; Published: February 2019
First available in Project Euclid: 12 December 2018

zbMATH: 07007199
MathSciNet: MR3892311
Digital Object Identifier: 10.3150/17-BEJ942

Keywords: $p$-value function , bounded parameter , deductive closure , deductive cogency , empty confidence set , Possibility theory , ranking function , ranking theory , restricted parameter space , surprise measure

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 1 • February 2019
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