Modified Simes' critical values under positive dependence

A modification of the critical values of Simes' test is suggested in this article when the underlying test statistics are multivariate normal with a common non-negative correlation, yielding a more powerful test than the original Simes' test. A step-up multiple testing procedure with these modified critical values, which is shown to control false discovery rate (FDR), is presented as a modification of the traditional Benjamini-Hochberg (BH) procedure. Simulations were carried out to compare this modified BH procedure with the BH and other modified BH procedures in terms of false non-discovery rate (FNR), 1-FDR-FNR and average power. The present modified BH procedure is observed to perform well compared to others when the test statistics are highly correlated and most of the hypotheses are true.