Open Access
October 2012 On false discovery rate thresholding for classification under sparsity
Pierre Neuvial, Etienne Roquain
Ann. Statist. 40(5): 2572-2600 (October 2012). DOI: 10.1214/12-AOS1042


We study the properties of false discovery rate (FDR) thresholding, viewed as a classification procedure. The “$0$”-class (null) is assumed to have a known density while the “$1$”-class (alternative) is obtained from the “$0$”-class either by translation or by scaling. Furthermore, the “$1$”-class is assumed to have a small number of elements w.r.t. the “$0$”-class (sparsity). We focus on densities of the Subbotin family, including Gaussian and Laplace models. Nonasymptotic oracle inequalities are derived for the excess risk of FDR thresholding. These inequalities lead to explicit rates of convergence of the excess risk to zero, as the number $m$ of items to be classified tends to infinity and in a regime where the power of the Bayes rule is away from $0$ and $1$. Moreover, these theoretical investigations suggest an explicit choice for the target level $\alpha_{m}$ of FDR thresholding, as a function of $m$. Our oracle inequalities show theoretically that the resulting FDR thresholding adapts to the unknown sparsity regime contained in the data. This property is illustrated with numerical experiments.


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Pierre Neuvial. Etienne Roquain. "On false discovery rate thresholding for classification under sparsity." Ann. Statist. 40 (5) 2572 - 2600, October 2012.


Published: October 2012
First available in Project Euclid: 4 February 2013

zbMATH: 1373.62315
MathSciNet: MR3097613
Digital Object Identifier: 10.1214/12-AOS1042

Primary: 62H30
Secondary: 62H15

Keywords: Adaptive procedure , Bayes’ rule , ‎classification‎ , False discovery rate , multiple testing , Oracle inequality , Sparsity

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 5 • October 2012
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