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

DOI10.3150/17-BEJ942OpenAlexW1532679648WikidataQ128785963 ScholiaQ128785963MaRDI QIDQ1715519

David R. Bickel, Alexandre G. Patriota

Publication date: 28 January 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bj/1544605238

zbMATH Keywords

possibility theoryranking functionrestricted parameter spacebounded parameterdeductive closure\(p\)-value functionranking theorydeductive cogencyempty confidence setsurprise measure

Mathematics Subject Classification ID

Parametric tolerance and confidence regions (62F25) Parametric hypothesis testing (62F03) Parametric inference under constraints (62F30) Bayesian inference (62F15) Axioms; other general questions in probability (60A05)

Related Items (9)

Maximum entropy derived and generalized under idempotent probability to address Bayes-frequentist uncertainty and model revision uncertainty: an information-theoretic semantics for possibility theory ⋮ Statistical evidence and surprise unified under possibility theory ⋮ Fisher's disjunction as the principle vindicating \(p\)-values, confidence intervals, and their generalizations: a frequentist semantics for possibility theory ⋮ Coherent Tests for Interval Null Hypotheses ⋮ The \(p\)-value interpreted as the posterior probability of explaining the data: applications to multiple testing and to restricted parameter spaces ⋮ Model fusion and multiple testing in the likelihood paradigm: shrinkage and evidence supporting a point null hypothesis ⋮ The sufficiency of the evidence, the relevancy of the evidence, and quantifying both with a single number ⋮ Coherent checking and updating of Bayesian models without specifying the model space: a decision-theoretic semantics for possibility theory ⋮ Interval estimation, point estimation, and null hypothesis significance testing calibrated by an estimated posterior probability of the null hypothesis

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