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October 2019 Test for high-dimensional correlation matrices
Shurong Zheng, Guanghui Cheng, Jianhua Guo, Hongtu Zhu
Ann. Statist. 47(5): 2887-2921 (October 2019). DOI: 10.1214/18-AOS1768

Abstract

Testing correlation structures has attracted extensive attention in the literature due to both its importance in real applications and several major theoretical challenges. The aim of this paper is to develop a general framework of testing correlation structures for the one , two and multiple sample testing problems under a high-dimensional setting when both the sample size and data dimension go to infinity. Our test statistics are designed to deal with both the dense and sparse alternatives. We systematically investigate the asymptotic null distribution, power function and unbiasedness of each test statistic. Theoretically, we make great efforts to deal with the nonindependency of all random matrices of the sample correlation matrices. We use simulation studies and real data analysis to illustrate the versatility and practicability of our test statistics.

Citation

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Shurong Zheng. Guanghui Cheng. Jianhua Guo. Hongtu Zhu. "Test for high-dimensional correlation matrices." Ann. Statist. 47 (5) 2887 - 2921, October 2019. https://doi.org/10.1214/18-AOS1768

Information

Received: 1 May 2017; Revised: 1 July 2018; Published: October 2019
First available in Project Euclid: 3 August 2019

zbMATH: 07114932
MathSciNet: MR3988776
Digital Object Identifier: 10.1214/18-AOS1768

Subjects:
Primary: 62H15
Secondary: 62H10

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • October 2019
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