  Since the work of \cite{Storey2004}, it is well-known that the performance of
the Benjamini-Hochberg (BH) procedure can be improved by incorporating
estimators of the number (or proportion) of null hypotheses, yielding an
adaptive BH procedure which still controls FDR. Several such plug-in estimators
have been proposed since then, for some of these, like Storey's estimator,
plug-in FDR control has been established, while for some others, e.g. the
estimator of \cite{PC2006}, some gaps remain to be closed. In this work we
introduce a unified class of estimators, which encompasses existing and new
estimators and unifies proofs of plug-in FDR control using simple convex
ordering arguments. We also show that any convex combination of such estimators
once more yields estimators with guaranteed plug-in FDR control. Additionally,
the flexibility of the new class of estimators also allows incorporating
distributional informations on the $p$-values. We illustrate this for the case
of discrete tests, where the null distributions of the $p$-values are typically
known. In that setting, we describe two generic approaches for adapting any
estimator from the general class to the discrete setting while guaranteeing
plug-in FDR control. While the focus of this paper is on presenting the
generality and flexibility of the new class of estimators, we also include some
analyses on simulated and real data.
