The Annals of Statistics

The sequential rejection principle of familywise error control

Jelle J. Goeman and Aldo Solari

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 38, Number 6 (2010), 3782-3810.

Dates
First available in Project Euclid: 30 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aos/1291126973

Digital Object Identifier
doi:10.1214/10-AOS829

Mathematical Reviews number (MathSciNet)
MR2766868

Zentralblatt MATH identifier
1204.62140

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62J15: Paired and multiple comparisons

Keywords
Multiple testing familywise error rate graph

Citation

Goeman, Jelle J.; Solari, Aldo. The sequential rejection principle of familywise error control. Ann. Statist. 38 (2010), no. 6, 3782--3810. doi:10.1214/10-AOS829. https://projecteuclid.org/euclid.aos/1291126973


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