Cohen et al. (2007) introduced the concept of a smooth multiple testing procedure and suggested a method for smoothing traditional stepwise procedures. We propose an alternative way of smoothing, which has some advantages over the CKS method.

This paper suggests two novel adaptive linear step-up procedures to reduce the bias of the estimator of π0, the proportion of true null hypotheses. Estimators of π0 are based on the number of p-values less than a threshold which converges to one.

We consider the class of monotone multiple testing procedures (monotone MTPs). It includes, among others, traditional step-down (Holm type) and step-up (Benjamini–Hochberg type) MTPs, as well as their generalization–step-up-down procedures (Tamhane et al., 1998). Our main result–the...