A Change-Point Approach to Estimating the Proportion of False Null Hypotheses in Multiple Testing

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 λ. 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 λ. 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.