## The Annals of Statistics

### On false discovery rate thresholding for classification under sparsity

#### Abstract

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.

#### Article information

Source
Ann. Statist. Volume 40, Number 5 (2012), 2572-2600.

Dates
First available in Project Euclid: 4 February 2013

https://projecteuclid.org/euclid.aos/1359987531

Digital Object Identifier
doi:10.1214/12-AOS1042

Mathematical Reviews number (MathSciNet)
MR3097613

Zentralblatt MATH identifier
06344386

#### Citation

Neuvial, Pierre; Roquain, Etienne. On false discovery rate thresholding for classification under sparsity. Ann. Statist. 40 (2012), no. 5, 2572--2600. doi:10.1214/12-AOS1042. https://projecteuclid.org/euclid.aos/1359987531

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#### Supplemental materials

• Supplementary material: Supplement to: On false discovery rate thresholding for classification under sparsity. Proofs, additional experiments and supplementary notes for the present paper.