Zhaochen Dong, Wei Yu, Wangli Xu

【Abstract】

Multiple test based on familywise error rate is a popular problem in statistical inference as testing the null hypothesis H-0=H-1 boolean AND H-2 boolean AND center dot center dot center dot boolean AND H-n is true versus the alternative that at least one hypothesis in H-1, H-2, horizontal ellipsis , H-n 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 tau(j) for the statistic with each j=1, horizontal ellipsis , 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.

【Keywords】

multiple testing, combined p-value method, test power, critical percentile parameter