Work

Exact calculations for false discovery proportion with application to least favorable configurations

Year: 2011

Type: article

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.

Source: The Annals of Statistics

DOI: 10.1214/10-aos847

Authors: Etienne Roquain, Fanny Villers

Institution: Université Pierre-et-Marie-Curie

Language: English

Topic: Statistical Methods in Clinical Trials

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Agence Nationale de la Recherche

Awards: Point processes, learning, nonparametric statistics and applications, DETECT: Nouvelles approches statistiques pour la vision artificielle et la bioinformatique