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April 2017 A rate optimal procedure for recovering sparse differences between high-dimensional means under dependence
Jun Li, Ping-Shou Zhong
Ann. Statist. 45(2): 557-590 (April 2017). DOI: 10.1214/16-AOS1459

Abstract

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.

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Jun Li. Ping-Shou Zhong. "A rate optimal procedure for recovering sparse differences between high-dimensional means under dependence." Ann. Statist. 45 (2) 557 - 590, April 2017. https://doi.org/10.1214/16-AOS1459

Information

Received: 1 November 2015; Revised: 1 February 2016; Published: April 2017
First available in Project Euclid: 16 May 2017

zbMATH: 1368.62152
MathSciNet: MR3650393
Digital Object Identifier: 10.1214/16-AOS1459

Subjects:
Primary: 62H15
Secondary: 62G20

Keywords: False discovery rate , high dimensional data , multiple testing , sparse signals , thresholding

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • April 2017
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