Modified estimator for the proportion of true null hypotheses under discrete setup with proven FDR control by the adaptive Benjamini-Hochberg procedure

Abstract

Some crucial issues about a recently proposed estimator for the proportion of true null hypotheses (${\pi }_0$) under discrete setup are discussed. An estimator for ${\pi }_0$ is introduced under the same setup. The estimator may be seen as a modification of a very popular estimator for ${\pi }_0$, originally proposed under the assumption of continuous test statistics. It is shown that adaptive Benjamini-Hochberg procedure remains conservative with the new estimator for ${\pi }_0$ being plugged in.

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