Plausibility functions and exact frequentist inference

TL;DR

This paper introduces a general framework for constructing exact frequentist inference procedures using plausibility functions, ensuring finite-sample validity without relying on asymptotic approximations.

Contribution

It develops a novel plausibility function-based approach for exact frequentist inference, including handling nuisance parameters, with demonstrated efficiency and broad applicability.

Findings

Methods are exact and valid in finite samples.

The approach is efficient across various problems.

Extension to nuisance parameters is effective.

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.