Independence test for high dimensional data based on regularized canonical correlation coefficients

Abstract

This paper proposes a new statistic to test independence between two high dimensional random vectors $\mathbf{X}:p_1\times 1$ and $\mathbf{Y}:p_2\times 1$. 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.

Published in at http://dx.doi.org/10.1214/14-AOS1284 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Independence test for high dimensional data based on regularized canonical correlation coefficients

Cited by in corpus (1)

• Independence test for high dimensional data based on regularized canonical correlation coefficients