A Practical Procedure to Find Matching Priors for Frequentist Inference

Abstract

We present a practical way to find matching priors via the use of saddlepoint approximations and obtain p-values of tests of an interest parameter in the presence of nuisance parameters. The advantages of our procedure are the flexibility in choosing different initial conditions so that one may adjust the performance of a test, and the less intensive computational efforts compared to a Markov Chain Monto Carlo method.

Keywords:

• Bayes
• Conditional inference
• Matching prior
• Modified signed root likelihood ratio statistic
• Partial differential equation
• Saddlepoint approximation

Mathematics Subject Classification:

• Primary 62E20
• Secondary 62C10

Acknowledgments

The authors were supported by grant DMS 0906569 from the National Science Foundation.

Notes

*I.C. stands for initial condition.

^†Results are based on 10,000 rounds of simulation with n = 30.

^‡Tests are of nominal Type I error 0.05.