RP-Estimation and RP-Testing for some nonparametric tests

Several RP-estimators for the Binomial, Sign, Wilcoxon Signed Rank, and Kendall tests are studied. Their behavior in terms of MSE is investigated, as well as their performancesfor RP-testing. Two classes of estimators are considered: the semi-parametric one, where RP-estimators are derived from the expression of the exact or approximated power function and the non-parametric one, whose RPestimators are obtained on the basis of the nonparametric plug-in principle. In order to evaluate the precision of RP-estimators for each test, the MSE is computed and the best overall estimator turns out to belong to the semi-parametric class. Then, in order to evaluate the RP-testing performances provided by RP estimators for each test, the disagreement between the RP-testing decision rule, i.e. “accept H0 if the RP-estimate is lower than, or equal to, 1/2, and reject H0 otherwise”, and the classical one (based on the critical value or on the p-value) is obtained. It is shown that the RP based testing decision for some semi-parametric RP estimators exactly replicates the classical one. In many situations, the RP-estimator replicating the classical decision rule also provides the best MSE.