Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests

Entropy

Lucio De Capitani¹  Daniele De Martini¹ 

[1] Department of Statistics and Quantitative Methods, University of Milano-Bicocca, via Bicocca degli Arcimboldi, 8, Milano 20126, Italy;

关键词: asymptotic power approximation;    sign test;    binomial test;    Wilcoxon signed rank test;    Kendall test;    stability of test outcomes;    reproducibility of tests outcomes;   

DOI  :  10.3390/e18040142

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown