High Dimensional Correlation Matrices: CLT and Its Applications

Jiti Gao, Xiao Han (), Guangming Pan () and Yanrong Yang ()

No 26/14, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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. (search for similar items in EconPapers)
JEL-codes: C21 C32 (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm and nep-tra
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Citations: View citations in EconPapers (1)

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