## The Annals of Statistics

### Test for high-dimensional correlation matrices

#### 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.

#### Article information

Source
Ann. Statist., Volume 47, Number 5 (2019), 2887-2921.

Dates
Revised: July 2018
First available in Project Euclid: 3 August 2019

https://projecteuclid.org/euclid.aos/1564797867

Digital Object Identifier
doi:10.1214/18-AOS1768

Mathematical Reviews number (MathSciNet)
MR3988776

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62H10: Distribution of statistics

#### Citation

Zheng, Shurong; Cheng, Guanghui; Guo, Jianhua; Zhu, Hongtu. Test for high-dimensional correlation matrices. Ann. Statist. 47 (2019), no. 5, 2887--2921. doi:10.1214/18-AOS1768. https://projecteuclid.org/euclid.aos/1564797867

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#### Supplemental materials

• Supplement to “Test for high-dimensional correlation matrices”. This supplementary material consists of the technical proofs and additional numerical results.