Open Access
Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Subjects:
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

JOURNAL ARTICLE
29 PAGES


SHARE
Vol.39 • No. 1 • February 2011
Back to Top