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2019 Dynamic adaptive procedures that control the false discovery rate
Peter W. MacDonald, Kun Liang, Arnold Janssen
Electron. J. Statist. 13(2): 3009-3024 (2019). DOI: 10.1214/19-EJS1589

Abstract

In the multiple testing problem with independent tests, the classical linear step-up procedure controls the false discovery rate (FDR) at level $\pi_{0}\alpha$, where $\pi_{0}$ is the proportion of true null hypotheses and $\alpha$ is the target FDR level. Adaptive procedures can improve power by incorporating estimates of $\pi_{0}$, which typically rely on a tuning parameter. Fixed adaptive procedures set their tuning parameters before seeing the data and can be shown to control the FDR in finite samples. We develop theoretical results for dynamic adaptive procedures whose tuning parameters are determined by the data. We show that, if the tuning parameter is chosen according to a stopping time rule, the corresponding dynamic adaptive procedure controls the FDR in finite samples. Examples include the recently proposed right-boundary procedure and the widely used lowest-slope procedure, among others. Simulation results show that the right-boundary procedure is more powerful than other dynamic adaptive procedures under independence and mild dependence conditions. The right-boundary procedure is implemented in the Bioconductor R package calm.

Citation

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Peter W. MacDonald. Kun Liang. Arnold Janssen. "Dynamic adaptive procedures that control the false discovery rate." Electron. J. Statist. 13 (2) 3009 - 3024, 2019. https://doi.org/10.1214/19-EJS1589

Information

Received: 1 June 2018; Published: 2019
First available in Project Euclid: 18 September 2019

zbMATH: 07113709
MathSciNet: MR4010590
Digital Object Identifier: 10.1214/19-EJS1589

Subjects:
Primary: 62G10
Secondary: 62F03, 62M02

JOURNAL ARTICLE
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Vol.13 • No. 2 • 2019
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