Plausibility functions and exact frequentist inference

Details Plausibility functions and exact frequentist inference Plausibility functions and exact frequentist inference

2012-03-29

arxiv.org/abs/1203.6665v1

Mathematics

Statistics Theory

23 pages, 4 figures, 3 tables

Scientific paper

In the frequentist program, inferential methods with exact control on error rates are a primary focus. Methods based on asymptotic distribution theory may not be suitable in a particular problem, in which case, a numerical method is needed. This paper presents a general, Monte Carlo-driven framework for the construction of frequentist procedures based on plausibility functions. It is proved that the suitably defined plausibility function-based tests and confidence regions have desired frequentist properties. Moreover, in an important special case involving likelihood ratios, conditions are given such that the plausibility function behaves asymptotically like a consistent Bayesian posterior distribution. An extension of the proposed method is also given for the case where nuisance parameters are present. A number of examples are given which illustrate the method and demonstrate its strong performance compared to other popular existing methods.

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