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 article 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.

• Bootstrap
• Confidence region
• Hypothesis test
• Likelihood
• Monte Carlo
• p-Value
• Profile likelihood

Additional information

Notes on contributors

Ryan Martin

Ryan Martin is Assistant Professor, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, IL 60607 (E-mail: [email protected]). The author is grateful for valuable comments from Chuanhai Liu, the editor, and the anonymous associate editor and referees. This research is partially supported by the National Science Foundation, grant DMS–1208833.