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

摘要

This paper proposes a new statistic to test independence between two highdimensional random vectors ${\mathbf{X}}:p_1\times1$ and${\mathbf{Y}}:p_2\times1$. The proposed statistic is based on the sum ofregularized sample canonical correlation coefficients of ${\mathbf{X}}$ and${\mathbf{Y}}$. The asymptotic distribution of the statistic under the nullhypothesis is established as a corollary of general central limit theorems(CLT) for the linear statistics of classical and regularized sample canonicalcorrelation coefficients when $p_1$ and $p_2$ are both comparable to the samplesize $n$. As applications of the developed independence test, various types ofdependent structures, such as factor models, ARCH models and a generaluncorrelated but dependent case, etc., are investigated by simulations. As anempirical application, cross-sectional dependence of daily stock returns ofcompanies between different sections in the New York Stock Exchange (NYSE) isdetected by the proposed test.