Small Sample Equivalence Tests for Exponentiality

• Activity Number: 78
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Renren Zhao*+ and Robert Paige
• Companies: and Missouri University of Science & Technology
• Keywords: equivalence tests ; exponentiality ; saddlepoint approximations ; uniformly most powerful test

Abstract

We consider small sample equivalence tests for exponentiality. Statistical inference in this setting is particularly challenging since equivalence testing procedures typically require a much larger sample sizes, in comparison with classical "difference tests", to perform well. We make use of Butler's marginal likelihood for the shape parameter of a gamma distribution in our development of small sample equivalence tests for exponentiality. We consider two procedures using the principle of confidence interval inclusion, four Bayesian methods, and the uniformly most powerful unbiased (UMPU) test where a saddlepoint approximation to the intractable distribution of a canonical sufficient statistic is used. We perform small sample simulation studies to assess the bias of our various tests and show that all of the Bayes posteriors we consider are integrable. Our simulation studies show that the saddlepoint-approximated UMPU method performs remarkably well for small sample sizes and is the only method which consistently exhibits an empirical significance level close to the nominal 5% level.