The Admissibility of the P-value for the Testing of Parameters in the Pareto Distribution

In this paper the problem of hypothesis testing is considered as an estimation problem within a decision-theoretic framework for estimating the accuracy of the test. The usual p-value is an admissible estimator for the one-sided testing of the scale parameter under the squared error loss function in the Pareto distribution. In the presence of nuisance parameter for model, the generalized p-value is inadmissible. Even though the usual p-value and the generalized p-value are inadmissible estimators for the one-sided testing of the shape parameter, it is difficult to exhibit a better estimator than the usual p-value. For the two-sided testing, although the usual p-value is generally inadmissible, it is remained as an estimator for the two-sided testing of the shape parameter.