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April 2015 Independence test for high dimensional data based on regularized canonical correlation coefficients
Yanrong Yang, Guangming Pan
Ann. Statist. 43(2): 467-500 (April 2015). DOI: 10.1214/14-AOS1284

Abstract

This paper proposes a new statistic to test independence between two high dimensional random vectors $\mathbf{X}:p_{1}\times1$ and $\mathbf{Y}:p_{2}\times1$. The proposed statistic is based on the sum of regularized sample canonical correlation coefficients of $\mathbf{X}$ and $\mathbf{Y}$. The asymptotic distribution of the statistic under the null hypothesis is established as a corollary of general central limit theorems (CLT) for the linear statistics of classical and regularized sample canonical correlation coefficients when $p_{1}$ and $p_{2}$ are both comparable to the sample size $n$. As applications of the developed independence test, various types of dependent structures, such as factor models, ARCH models and a general uncorrelated but dependent case, etc., are investigated by simulations. As an empirical application, cross-sectional dependence of daily stock returns of companies between different sections in the New York Stock Exchange (NYSE) is detected by the proposed test.

Citation

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Yanrong Yang. Guangming Pan. "Independence test for high dimensional data based on regularized canonical correlation coefficients." Ann. Statist. 43 (2) 467 - 500, April 2015. https://doi.org/10.1214/14-AOS1284

Information

Published: April 2015
First available in Project Euclid: 24 February 2015

zbMATH: 1344.60027
MathSciNet: MR3316187
Digital Object Identifier: 10.1214/14-AOS1284

Subjects:
Primary: 60K35

Keywords: Canonical correlation coefficients , central limit theorem , Independence test , large dimensional random matrix theory , Linear spectral statistics

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 2 • April 2015
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