| The false discovery rate (FDR) is a widely used error measure in multiple testing. Adaptive FDR procedures, incorporating a conservative estimator of the proportion of true null hypotheses, are usually more powerful than their non-adaptive counterparts. However, their performances depend critically on the test statistics having continuous distributions with very restrictive dependencies. Recent genomic sequencing technologies such as microarray and next-generation sequencing have generated massive data sets from which statistical analyses produce discrete test statistics and continuous test statistics bearing unknown and strong dependency. These two features have been known to have adverse effects on existing FDR procedures. Towards this end, better adaptive FDR procedures for discrete and for dependent continuous test statistics are needed. For multiple testing based on p-values from discrete test statistics whose null distributions dominate the uniform distribution, new estimators of the proportion of true null hypotheses and of the FDRs of one-step multiple testing procedures (MTPs) are proposed. Further, to better estimate the FDRs of one-step MTPs when testing normal means under dependence, a (uniformly) consistent estimator of the proportion of nonzero normal means, when the test statistics follow a joint normal distribution whose known covariance matrix represents strong dependencies of a certain type, has been developed. Improved performances of these new estimators have been justied both theoretically and empirically. |
