Bernoulli

Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters

David R. Bickel and Alexandre G. Patriota

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Abstract

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.

Article information

Source
Bernoulli, Volume 25, Number 1 (2019), 47-74.

Dates
Received: December 2014
Revised: March 2017
First available in Project Euclid: 12 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1544605238

Digital Object Identifier
doi:10.3150/17-BEJ942

Zentralblatt MATH identifier
07007199

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

Citation

Bickel, David R.; Patriota, Alexandre G. Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters. Bernoulli 25 (2019), no. 1, 47--74. doi:10.3150/17-BEJ942. https://projecteuclid.org/euclid.bj/1544605238


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