Estimating the proportion of true null hypotheses and adaptive false discovery rate control in discrete paradigm

Storey's estimator for the proportion of true null hypotheses, originally proposed under the continuous framework, has been modified in this work under the discrete framework. The modification results in improved estimation of the parameter of interest. The proposed estimator is used to formulate an adaptive version of the Benjamini–Hochberg procedure. Control over the false discovery rate by the proposed adaptive procedure has been proved analytically. The proposed estimate is also used to formulate an adaptive version of the Benjamini–Hochberg–Heyse procedure. Simulation experiments establish the conservative nature of this new adaptive procedure. Substantial amount of gain in power is observed for the new adaptive procedures over the standard procedures. For demonstration of the proposed method, two important real life gene expression data sets, one related to the study of HIV and the other related to methylation study, are used.