## Bernoulli

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

#### 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
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

Mathematical Reviews number (MathSciNet)
MR3892311

Zentralblatt MATH identifier
07007199

#### 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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