Plausibility functions and exact frequentist inference

Abstract

In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This paper presents a general framework for the construction of exact frequentist procedures based on plausibility functions. It is shown that the plausibility function-based tests and confidence regions have the desired frequentist properties in finite samples---no large-sample justification needed. An extension of the proposed method is also given for problems involving nuisance parameters. Examples demonstrate that the plausibility function-based method is both exact and efficient in a wide variety of problems.

21 pages, 5 figures, 3 tables

References in corpus (4)

• Inferential models: A framework for prior-free posterior probabilistic inference
• Marginal inferential models: prior-free probabilistic inference on interest parameters
• Conditional inferential models: combining information for prior-free probabilistic inference
• A note on p-values interpreted as plausibilities

Cited by in corpus (18)

• Inferential models: A framework for prior-free posterior probabilistic inference
• A note on p-values interpreted as plausibilities
• On an inferential model construction using generalized associations
• Frameworks for prior-free posterior probabilistic inference
• Validity, consonant plausibility measures, and conformal prediction
• Valid inferential models for prediction in supervised learning problems
• Direct and approximately valid probabilistic inference on a class of statistical functionals
• A statistical inference course based on p-values
• Generalized inferential models for censored data
• A mathematical characterization of confidence as valid belief
• Asymptotic efficiency of inferential models and a possibilistic Bernstein--von Mises theorem
• Possibilistic inferential models: a review
• Stochastic optimization for numerical evaluation of imprecise probabilities
• Computationally efficient variational-like approximations of possibilistic inferential models
• Large-sample theory for inferential models: a possibilistic Bernstein--von Mises theorem
• Generalized inferential models for meta-analyses based on few studies
• Exact model comparisons in the plausibility framework
• A simple recipe for making accurate parametric inference in finite sample