A Change-Point Approach to Estimating the Proportion of False Null Hypotheses in Multiple Testing
arxiv(2023)
Abstract
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.
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