A RATE OPTIMAL PROCEDURE FOR RECOVERING SPARSE DIFFERENCES BETWEEN HIGH-DIMENSIONAL MEANS UNDER DEPENDENCE

• 成果类型: Article
• 署名作者: Li, Jun; Zhong, Ping-Shou
• 署名单位: University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Michigan State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1459
• 发表日期: 2017
• 页码: 557-590
• 关键词: false discovery rate; Covariance matrices; HIGHER CRITICISM; EQUALITY; tests; graph

摘要

The paper considers the problem of recovering the sparse different components between two high-dimensional means of column-wise dependent random vectors. We show that dependence can be utilized to lower the identification boundary for signal recovery. Moreover, an optimal convergence rate for the marginal false nondiscovery rate (mFNR) is established under dependence. The convergence rate is faster than the optimal rate without dependence. To recover the sparse signal bearing dimensions, we propose a Dependence-Assisted Thresholding and Excising (DATE) procedure, which is shown to be rate optimal for the mFNR with the marginal false discovery rate (mFDR) controlled at a pre-specified level. Extensions of the DATE to recover the differences in contrasts among multiple population means and differences between two covariance matrices are also provided. Simulation studies and case study are given to demonstrate the performance of the proposed signal identification procedure.