Change-Point Ideas in Multiple Testing: estimating the proportion of false null hypotheses

Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses is an important problem in multiple testing literature. In the sequence of sorted p-values (p-value plot), false null p-values tend to be smaller and concentrated at the beginning. This suggests approximate piecewise linear shape of the p-value plot, with change-point in slope separating small from large p-values. We propose a method for estimating the false null proportion (Difference Of Slopes) that utilizes the idea of estimating that change-point in the p-value plot.