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December 2010 The sequential rejection principle of familywise error control
Jelle J. Goeman, Aldo Solari
Ann. Statist. 38(6): 3782-3810 (December 2010). DOI: 10.1214/10-AOS829


Closed testing and partitioning are recognized as fundamental principles of familywise error control. In this paper, we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing. We present a general sequentially rejective multiple testing procedure and show that many well-known familywise error controlling methods can be constructed as special cases of this procedure, among which are the procedures of Holm, Shaffer and Hochberg, parallel and serial gatekeeping procedures, modern procedures for multiple testing in graphs, resampling-based multiple testing procedures and even the closed testing and partitioning procedures themselves. We also give a general proof that sequentially rejective multiple testing procedures strongly control the familywise error if they fulfill simple criteria of monotonicity of the critical values and a limited form of weak familywise error control in each single step. The sequential rejection principle gives a novel theoretical perspective on many well-known multiple testing procedures, emphasizing the sequential aspect. Its main practical usefulness is for the development of multiple testing procedures for null hypotheses, possibly logically related, that are structured in a graph. We illustrate this by presenting a uniform improvement of a recently published procedure.


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Jelle J. Goeman. Aldo Solari. "The sequential rejection principle of familywise error control." Ann. Statist. 38 (6) 3782 - 3810, December 2010.


Published: December 2010
First available in Project Euclid: 30 November 2010

zbMATH: 1204.62140
MathSciNet: MR2766868
Digital Object Identifier: 10.1214/10-AOS829

Primary: 62H15
Secondary: 62J15

Keywords: familywise error rate , graph , multiple testing

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 6 • December 2010
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