Open Access
June 2009 A new multiple testing method in the dependent case
Arthur Cohen, Harold B. Sackrowitz, Minya Xu
Ann. Statist. 37(3): 1518-1544 (June 2009). DOI: 10.1214/08-AOS616


The most popular multiple testing procedures are stepwise procedures based on P-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini–Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300] and their offsprings. Even for models that entail dependent data, P-values based on marginal distributions are used. Unlike such methods, the new method takes dependency into account at all stages. Furthermore, the P-value procedures often lack an intuitive convexity property, which is needed for admissibility. Still further, the new methodology is computationally feasible. If the number of tests is large and the proportion of true alternatives is less than say 25 percent, simulations demonstrate a clear preference for the new methodology. Applications are detailed for models such as testing treatments against control (or any intraclass correlation model), testing for change points and testing means when correlation is successive.


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Arthur Cohen. Harold B. Sackrowitz. Minya Xu. "A new multiple testing method in the dependent case." Ann. Statist. 37 (3) 1518 - 1544, June 2009.


Published: June 2009
First available in Project Euclid: 10 April 2009

zbMATH: 1161.62040
MathSciNet: MR2509082
Digital Object Identifier: 10.1214/08-AOS616

Primary: 62F03
Secondary: 62J15

Keywords: Admissibility , change point problem , False discovery rate , likelihood ratio , residuals , step-down procedure , step-up procedure , successive correlation model , treatments vs. control , two-sided alternatives , vector risk

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 3 • June 2009
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