ON FALSE DISCOVERY RATE THRESHOLDING FOR CLASSIFICATION UNDER SPARSITY

• 成果类型: Article
• 署名作者: Neuvial, Pierre; Roquain, Etienne
• 署名单位: INRAE; Universite Paris Saclay; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1042
• 发表日期: 2012
• 页码: 2572-2600
• 关键词: multiple testing procedures; EMPIRICAL BAYES; FDR CONTROL; INDEPENDENCE; microarrays

摘要

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 am 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.