Statistics and Its Interface

Volume 6 (2013)

Number 1

On permutation procedures for strong control in multiple testing with gene expression data

Pages: 79 – 89

DOI: http://dx.doi.org/10.4310/SII.2013.v6.n1.a8

Authors

Grzegorz A. Rempala (Department of Biostatistics and Cancer Research Center, Georgia Health Sciences University, U.S.A.)

Yuhong Yang (School of Statistics, University of Minnesota, U.S.A.)

Abstract

We consider two popular, permutation-based, step-down procedures of $p$-values adjustment in multiple testing problems known as min $P$ and max $T$ and intended for strong control of the family-wise error rate, under the so-called subset pivotality property (SPP). We examine key but subtle issues involved in ascertaining validity of these methods, and also introduce a new, slightly narrower notion of strong control which ensures proper bounds on the family-wise error rate in min $P$ and max $T$ without SPP.

Keywords

multiple testing, strong control of family-wise error rate, step down p-value adjustment methods, subset pivotality property, permutation test

2010 Mathematics Subject Classification

Primary 62H15, 62J15. Secondary 92D10.

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