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2017 The control of the false discovery rate in fixed sequence multiple testing
Gavin Lynch, Wenge Guo, Sanat K. Sarkar, Helmut Finner
Electron. J. Statist. 11(2): 4649-4673 (2017). DOI: 10.1214/17-EJS1359

Abstract

Controlling false discovery rate (FDR) is a powerful approach to multiple testing. In many applications, the tested hypotheses have an inherent hierarchical structure. In this paper, we focus on the fixed sequence structure where the testing order of the hypotheses has been strictly specified in advance. We are motivated to study such a structure, since it is the most basic of hierarchical structure, yet it is often seen in real applications such as statistical process control and streaming data analysis. We first consider a conventional fixed sequence method that stops testing once an acceptance occurs, and develop such a method controlling FDR under both arbitrary and negative dependencies. The method under arbitrary dependency is shown to be unimprovable without losing control of FDR and, unlike existing FDR methods; it cannot be improved even by restricting to the usual positive regression dependence on subset (PRDS) condition. To account for any potential mistakes in the ordering of the tests, we extend the conventional fixed sequence method to one that allows more but a given number of acceptances. Simulation studies show that the proposed procedures can be powerful alternatives to existing FDR controlling procedures. The proposed procedures are illustrated through a real data set from a microarray experiment.

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Gavin Lynch. Wenge Guo. Sanat K. Sarkar. Helmut Finner. "The control of the false discovery rate in fixed sequence multiple testing." Electron. J. Statist. 11 (2) 4649 - 4673, 2017. https://doi.org/10.1214/17-EJS1359

Information

Received: 1 November 2016; Published: 2017
First available in Project Euclid: 18 November 2017

zbMATH: 06816628
MathSciNet: MR3724971
Digital Object Identifier: 10.1214/17-EJS1359

Subjects:
Primary: 62J15

JOURNAL ARTICLE
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Vol.11 • No. 2 • 2017
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