  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.
