The admissibility of the p-value for the testing of parameters in the Pareto distribution

Abstract

In this paper the problem of hypothesis testing is consid-ered as an estimation problem within a decision-theoretic framework forestimating the accuracy of the test. The usual p-value is an admissi-ble estimator for the one-sided testing of the scale parameter under thesquared error loss function in the Pareto distribution. In the presence ofnuisance parameter for model, the generalized p-value is inadmissible.Even though the usual p-value and the generalized p-value are inadmis-sible estimators for the one-sided testing of the shape parameter, it isdicult to exhibit a better estimator than the usual p-value. For thetwo-sided testing, although the usual p-value is generally inadmissible, ithas been shown that the usual p-value as an estimator for the two-sidedtesting of the shape parameter may not be too bad.