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

Anica Kostic; Piotr Fryzlewicz

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arXiv · 2309.10017

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

Anica Kostic·Piotr Fryzlewicz

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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 $\lambda$. 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.

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Anica Kostic, Piotr Fryzlewicz. 2023-09-18. A Change-Point Approach to Estimating the Proportion of False Null Hypotheses in Multiple Testing. https://arxiv.org/abs/2309.10017

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