Improved estimation of accuracy in simple hypothesis versus simple alternative testing

In the hypothesis testing problem, a most common used evidence against the null hypothesis is the p-value. Although there have been many Bayesian criticisms leveled at p-value, Hwang et al. (Ann. Statist. 20 (1992), 490) show the adequacy of using p-value as evidence against the null hypothesis by considering testing as an estimation problem. However, when the parameter space is not the natural space, Woodroofe and Wang (Ann. Statist. 28 (2000) 1561) show that the usual p-value derived by the N–P test is not appropriate to be the evidence against the null hypothesis for the Poisson distribution from an estimation point of view and provide a modified p-value. Although this modified p-value is admissible, it is not the admissible estimator which can dominate the usual p-value. In this paper, we concentrate on the simple hypothesis versus simple alternative hypothesis testing problem. Admissible estimators which dominate the usual p-value are provided.