The admissibility of the \(p\)-value for the testing of parameters in the Pareto distribution. (English) Zbl 1491.62017
Summary: In this paper the problem of hypothesis testing is considered as an estimation problem within a decision-theoretic framework forestimating 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 has been shown that the usual \(p\)-value as an estimator for the two-sided testing of the shape parameter may not be too bad.
MSC:
| 62F03 | Parametric hypothesis testing |
| 62F15 | Bayesian inference |
| 62C15 | Admissibility in statistical decision theory |
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