Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests
Several reproducibility probability (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 performances for RP-testing. Two classes of estimators are considered: the semi-parametric one, where RP-es...
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doaj-cce8848ce8bb4959ba2849ea136b98862020-11-24T23:21:58ZengMDPI AGEntropy1099-43002016-04-0118414210.3390/e18040142e18040142Reproducibility Probability Estimation and RP-Testing for Some Nonparametric TestsLucio De Capitani0Daniele De Martini1Department of Statistics and Quantitative Methods, University of Milano-Bicocca, via Bicocca degli Arcimboldi, 8, Milano 20126, ItalyDepartment of Statistics and Quantitative Methods, University of Milano-Bicocca, via Bicocca degli Arcimboldi, 8, Milano 20126, ItalySeveral reproducibility probability (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 performances for 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 RP-estimators 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.http://www.mdpi.com/1099-4300/18/4/142asymptotic power approximationsign testbinomial testWilcoxon signed rank testKendall teststability of test outcomesreproducibility of tests outcomes |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lucio De Capitani Daniele De Martini |
spellingShingle |
Lucio De Capitani Daniele De Martini Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests Entropy asymptotic power approximation sign test binomial test Wilcoxon signed rank test Kendall test stability of test outcomes reproducibility of tests outcomes |
author_facet |
Lucio De Capitani Daniele De Martini |
author_sort |
Lucio De Capitani |
title |
Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests |
title_short |
Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests |
title_full |
Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests |
title_fullStr |
Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests |
title_full_unstemmed |
Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests |
title_sort |
reproducibility probability estimation and rp-testing for some nonparametric tests |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2016-04-01 |
description |
Several reproducibility probability (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 performances for 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 RP-estimators 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. |
topic |
asymptotic power approximation sign test binomial test Wilcoxon signed rank test Kendall test stability of test outcomes reproducibility of tests outcomes |
url |
http://www.mdpi.com/1099-4300/18/4/142 |
work_keys_str_mv |
AT luciodecapitani reproducibilityprobabilityestimationandrptestingforsomenonparametrictests AT danieledemartini reproducibilityprobabilityestimationandrptestingforsomenonparametrictests |
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1725569199163572224 |