988 research outputs found
Independence test for high dimensional data based on regularized canonical correlation coefficients
This paper proposes a new statistic to test independence between two high
dimensional random vectors and
. The proposed statistic is based on the sum of
regularized sample canonical correlation coefficients of and
. 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 and are both comparable to the sample
size . 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.Comment: 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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