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.

DE CAPITANI, L., DE MARTINI, D. (2015). RP-Estimation and RP-Testing for some nonparametric tests [Working paper del dipartimento].

RP-Estimation and RP-Testing for some nonparametric tests

DE CAPITANI, LUCIO
Primo
;
DE MARTINI, DANIELE
2015

Abstract

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.
Working paper del dipartimento
Asymptotic power approximation,Sign Test, Binomial Test, Wilcoxon Signed Rank Test, Kendall Test, Stability of test outcomes, Reproducibility of tests outcomes
English
2015
DE CAPITANI, L., DE MARTINI, D. (2015). RP-Estimation and RP-Testing for some nonparametric tests [Working paper del dipartimento].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/96394
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