  For estimating the proportion of false null hypotheses in multiple testing, a
family of estimators by Storey (2002) is widely used in the applied and
statistical literature, with many methods suggested for selecting the parameter
$\lambda$. Inspired by change-point concepts, our new approach to the latter
problem first approximates the $p$-value plot with a piecewise linear function
with a single change-point and then selects the $p$-value at the change-point
location as $\lambda$. Simulations show that our method has among the smallest
RMSE across various settings, and we extend it to address the estimation in
cases of superuniform $p$-values. We provide asymptotic theory for our
estimator, relying on the theory of quantile processes. Additionally, we
propose an application in the change-point literature and illustrate it using
high-dimensional CNV data.
