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Multiple permutation testing is a test method combining the idea of permutation and multiple testing. It first employs the permutation testing to calculate p-values for single tests, and then determines the result based on criteria of multiple testing. To well control type I error rate, the classical method needs a large number of permutation samples for calculating p-values. When the dimension of data, m, is high, the permutation procedure is very time consuming. This paper proposes a components-combined algorithm for the type I error rate control. The new algorithm only requires a small and fixed number of permutation samples for any dimension of data and can achieve the same approximation accuracy of p-values as the classical method. Therefore, it reduces the computational amount of multiple permutation testing procedures from to . The algorithm is then applied to several testing problems and the power performance is examined by simulations and comparisons with existing methods. [ABSTRACT FROM AUTHOR]

Multiple test based on familywise error rate is a popular problem in statistical inference as testing the null hypothesisH0=H1∩H2∩···∩Hnis true versus the alternative that at least one hypothesis inH1,H2, … ,Hnis false. Classical tests include the Bonferroni test and the Simes test. So far, the most efficient methods for this problem are known as the combinedp-value tests, such as the Fisher's product test, the truncated product method, the rank truncated product test, the adaptive rank truncated product (ARTP) method and Zhang et al.’s [A combinedp-value test for multiple hypothesis testing. J Stat Plan Inference. 2013;143:764–770] test that extends the ARTP method. Our method is based on Zhang et al.’s [A combinedp-value test for multiple hypothesis testing. J Stat Plan Inference. 2013;143:764–770] test and modifies it by using different critical percentile parameter τjfor the statisticwith eachj=1, … ,n. Simulation studies show that the sizes of our test are stable at the significance level and the powers are superior to commonly used methods. [ABSTRACT FROM PUBLISHER]