RANK: Large-Scale Inference With Graphical Nonlinear Knockoffs

• 成果类型: Article
• 署名作者: Fan, Yingying; Demirkaya, Emre; Li, Gaorong; Lv, Jinchi
• 署名单位: University of Southern California; University of Tennessee System; University of Tennessee Knoxville; Beijing University of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1546589
• 发表日期: 2020
• 页码: 362-379
• 关键词: false discovery rate; variable selection; unknown sparsity; regression; tests; identification; bootstrap; rates

摘要

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this article, we provide theoretical foundations on the power and robustness for the model-X knockoffs procedure introduced recently in Candes, Fan, Janson and Lv in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-X knockoffs method called graphical nonlinear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real dataset is analyzed to further assess the performance of the suggested knockoffs procedure. for this article are available online.