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

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Title: Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters
Authors: Bickel, David R.
Date: 2014-08-19
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.
URL: http://hdl.handle.net/10393/31530
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CollectionMathématiques et statistiques // Mathematics and Statistics
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