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Some crucial issues about a recently proposed estimator for the proportion oftrue null hypotheses ($\pi_0$) under discrete setup are discussed. An estimatorfor $\pi_0$ is introduced under the same setup. The estimator may be seen as amodification of a very popular estimator for $\pi_0$, originally proposed underthe assumption of continuous test statistics. It is shown that adaptiveBenjamini-Hochberg procedure remains conservative with the new estimator for$\pi_0$ being plugged in.

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