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.
Publié le : 2011-02-15
Classification:
False discovery rate,
false discovery proportion,
multiple testing,
least favorable configuration,
power,
equicorrelated multivariate normal distribution,
step-up,
step-down,
62J15,
62G10,
60C05
@article{1297779857,
author = {Roquain, Etienne and Villers, Fanny},
title = {Exact calculations for false discovery proportion with application to least favorable configurations},
journal = {Ann. Statist.},
volume = {39},
number = {1},
year = {2011},
pages = { 584-612},
language = {en},
url = {http://dml.mathdoc.fr/item/1297779857}
}
Roquain, Etienne; Villers, Fanny. Exact calculations for false discovery proportion with application to least favorable configurations. Ann. Statist., Tome 39 (2011) no. 1, pp. 584-612. http://gdmltest.u-ga.fr/item/1297779857/