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

Author(s)

Bickel, David R. ^{[1, 2]} ; Patriota, Alexandre G. ^[3]

Affiliation

^[1] Univ Ottawa, Ottawa Inst Syst Biol, Dept Biochem Microbiol & Immunol, 451 Smyth Rd, Ottawa, ON K1H 8M5 - Canada

^[2] Univ Ottawa, Dept Math & Stat, 585 King Edward, Ottawa, ON K1N 6N5 - Canada

^[3] Univ Sao Paulo, Inst Math & Stat, Dept Stat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

• Document type: Journal article
• Source: BERNOULLI; v. 25, n. 1, p. 47-74, FEB 2019.
• Web of Science Citations: 1

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. (AU)

• FAPESP's process: 14/25595-0 - Comparisons between the s-value and some classical measures of evidences
• Grantee: Alexandre Galvão Patriota
• Support Opportunities: Scholarships abroad - Research