Institute of Mathematical Statistics Lecture Notes - Monograph Series

Weighted FWE-controlling methods in high-dimensional situations

Peter H. Westfall, Siegfried Kropf, and Livio Finos

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With high dimensionality, standard Bonferroni-style procedures can suffer from loss of power, since the significance level $\alpha$ must be divided by $k$ to declare significance. Kropf and Läuter (KL) show that certain data-dependent quadratic forms can be used to "pre-specify hypotheses, which can then be tested in a fixed, data-dependent order, without multiplicity adjustment. In this article we extend the KL procedure to a class of weighted procedures, using the same quadratic forms. The class includes the KL method, the Bonferroni-Holm method, and other, new procedures. We establish strong FWE control for all procedures, and compare power and level of various weighting methods using analytical and simulation results. The method is applied using a high-dimensional mixture model that is suggested by the analysis of real gene expression data.

Chapter information

Y. Benjamini, F. Bretz and S. Sarkar, eds., Recent Developments in Multiple Comparison Procedures (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 143-154

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F03: Hypothesis testing 62F07: Ranking and selection
Secondary: 62C25: Compound decision problems 62E17: Approximations to distributions (nonasymptotic)

a-priori ordered hypotheses gene expression multiple comparisons

Copyright © 2004, Institute of Mathematical Statistics


Westfall, Peter H.; Kropf, Siegfried; Finos, Livio. Weighted FWE-controlling methods in high-dimensional situations. Recent Developments in Multiple Comparison Procedures, 143--154, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2004. doi:10.1214/lnms/1196285632.

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