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February 2011 Exact calculations for false discovery proportion with application to least favorable configurations
Etienne Roquain, Fanny Villers
Ann. Statist. 39(1): 584-612 (February 2011). DOI: 10.1214/10-AOS847


In a context of multiple hypothesis testing, we provide several new exact calculations related to the false discovery proportion (FDP) of step-up and step-down procedures. For step-up procedures, we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable, which leads to explicit computations of the c.d.f., the sth moment and the mean of the FDP, the latter corresponding to the false discovery rate (FDR). For step-down procedures, we derive what is to our knowledge the first explicit formula for the FDR valid for any alternative c.d.f. of the p-values. We also derive explicit computations of the power for both step-up and step-down procedures. These formulas are “explicit” in the sense that they only involve the parameters of the model and the c.d.f. of the order statistics of i.i.d. uniform variables. The p-values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true/false hypotheses is used. Our approach is then used to investigate new results which are of interest in their own right, related to least/most favorable configurations for the FDR and the variance of the FDP.


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Etienne Roquain. Fanny Villers. "Exact calculations for false discovery proportion with application to least favorable configurations." Ann. Statist. 39 (1) 584 - 612, February 2011.


Published: February 2011
First available in Project Euclid: 15 February 2011

zbMATH: 1209.62164
MathSciNet: MR2797857
Digital Object Identifier: 10.1214/10-AOS847

Primary: 62J15
Secondary: 60C05 , 62G10

Keywords: equicorrelated multivariate normal distribution , false discovery proportion , False discovery rate , least favorable configuration , multiple testing , power , step-down , step-up

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 1 • February 2011
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