A modified combinedp-value multiple test

Multiple test based on familywise error rate is a popular problem in statistical inference as testing the null hypothesis H0=H1∩H2∩···∩Hn is true versus the alternative that at least one hypothesis in H1, H2, … , Hn is false. Classical tests include the Bonferroni test and the Simes test. So far, the most efficient methods for this problem are known as the combined p-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 combined p-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 combined p-value test for multiple hypothesis testing. J Stat Plan Inference. 2013;143:764–770] test and modifies it by using different critical percentile parameter τj for the statistic Wj=∏i=1jp(i) with each j=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.