Open Access
February 2006 False discovery and false nondiscovery rates in single-step multiple testing procedures
Sanat K. Sarkar
Ann. Statist. 34(1): 394-415 (February 2006). DOI: 10.1214/009053605000000778


Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR and FNR and related measures. First, considering fixed configurations of true and false null hypotheses, inequalities are obtained to explain how an FDR- or FNR-controlling single-step procedure, such as a Bonferroni or Šidák procedure, can potentially be improved. Two families of procedures are then constructed, one that modifies the FDR-controlling and the other that modifies the FNR-controlling Šidák procedure. These are proved to control FDR or FNR under independence less conservatively than the corresponding families that modify the FDR- or FNR-controlling Bonferroni procedure. Results of numerical investigations of the performance of the modified Šidák FDR procedure over its competitors are presented. Second, considering a mixture model where different configurations of true and false null hypotheses are assumed to have certain probabilities, results are also derived that extend some of Storey’s work to the dependence case.


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Sanat K. Sarkar. "False discovery and false nondiscovery rates in single-step multiple testing procedures." Ann. Statist. 34 (1) 394 - 415, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62060
MathSciNet: MR2275247
Digital Object Identifier: 10.1214/009053605000000778

Primary: 62H15 , 62J15
Secondary: 62H99

Keywords: mixture model , Modified Bonferroni and Šidák procedures , positive false discovery rate , positive false nondiscovery rate

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 1 • February 2006
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