High Dimensional Correlation Matrices: CLT and Its Applications

55 Pages Posted: 10 Nov 2014

See all articles by Jiti Gao

Jiti Gao

Monash University - Department of Econometrics & Business Statistics

Xiao Han

Nanyang Technological University (NTU)

Guangming Pan

Nanyang Technological University (NTU)

Yanrong Yang

Monash University - Department of Econometrics & Business Statistics

Date Written: November 9, 2014

Abstract

Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, this paper establishes a new central limit theorem (CLT) for a linear spectral statistic (LSS) of high dimensional sample correlation matrices for the case where the dimension p and the sample size n are comparable. This result is of independent interest in large dimensional random matrix theory. Meanwhile, we apply the linear spectral statistic to an independence test for p random variables, and then an equivalence test for p factor loadings and n factors in a factor model. The finite sample performance of the proposed test shows its applicability and effectiveness in practice. An empirical application to test the independence of household incomes from different cities in China is also conducted.

Keywords: Central limit theorem; equivalence test; high dimensional correlation matrix; independence test; linear spectral statistics

JEL Classification: C21, C32

Suggested Citation

Gao, Jiti and Han, Xiao and Pan, Guangming and Yang, Yanrong, High Dimensional Correlation Matrices: CLT and Its Applications (November 9, 2014). Available at SSRN: https://ssrn.com/abstract=2521247 or http://dx.doi.org/10.2139/ssrn.2521247

Jiti Gao (Contact Author)

Monash University - Department of Econometrics & Business Statistics ( email )

900 Dandenong Road
Caulfield East, Victoria 3145
Australia
61399031675 (Phone)
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HOME PAGE: http://www.jitigao.com

Xiao Han

Nanyang Technological University (NTU) ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

Guangming Pan

Nanyang Technological University (NTU) ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

Yanrong Yang

Monash University - Department of Econometrics & Business Statistics ( email )

Wellington Road
Clayton, Victoria 3168
Australia

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