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December 2020 Simultaneous high-probability bounds on the false discovery proportion in structured, regression and online settings
Eugene Katsevich, Aaditya Ramdas
Ann. Statist. 48(6): 3465-3487 (December 2020). DOI: 10.1214/19-AOS1938


While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (Statist. Sci. 26 (2011) 584–597) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds on the false discovery proportion (FDP) of the chosen set. In this paper, we propose a new class of such simultaneous FDP bounds, tailored for nested sequences of rejection sets. While most existing simultaneous FDP bounds are based on closed testing using global null tests based on sorted $p$-values, we additionally consider the setting where side information can be leveraged to boost power, the variable selection setting where knockoff statistics can be used to order variables, and the online setting where decisions about rejections must be made as data arrives. Our finite-sample, closed form bounds are based on repurposing the FDP estimates from false discovery rate (FDR) controlling procedures designed for each of the above settings. These results establish a novel connection between the parallel literatures of simultaneous FDP bounds and FDR control methods, and use proof techniques employing martingales and filtrations that are new to both these literatures. We demonstrate the utility of our results by augmenting a recent knockoffs analysis of the UK Biobank dataset.


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Eugene Katsevich. Aaditya Ramdas. "Simultaneous high-probability bounds on the false discovery proportion in structured, regression and online settings." Ann. Statist. 48 (6) 3465 - 3487, December 2020.


Received: 1 March 2018; Revised: 1 December 2019; Published: December 2020
First available in Project Euclid: 11 December 2020

Digital Object Identifier: 10.1214/19-AOS1938

Primary: 62F03 , 62J15
Secondary: 60G42 , 62P10

Keywords: false discovery exceedance , False discovery rate , FDR , FDX , multiple testing , post hoc confidence bounds , uniform martingale concentration

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.48 • No. 6 • December 2020
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