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Title: Testing independence in high-dimensional data: $\rho$V-coefficient based approach Authors:  Takahiro Nishiyama - Senshu University (Japan) [presenting]
Masashi Hyodo - Osaka Prefecture University (Japan)
Tatjana Pavlenko - KTH Royal Institute of Technology (Sweden)
Abstract: The problem of testing mutual independence of $k$ high-dimensional random vectors is considered when the data are multivariate normal and $k$ $\geq$ $2$ is a fixed integer. For this purpose, we focus on the vector correlation coefficient, $\rho$V and propose an extension of its classical estimator which is constructed to correct potential sources of inconsistency related to the high dimensionality. Building on the proposed estimator of $\rho$V, we derive the new test statistic and study its limiting behavior in a general high-dimensional asymptotic framework which allows the vector's dimensionality arbitrarily exceeds the sample size. Specifically, we show that the asymptotic distribution of the test statistic under the main hypothesis of independence is standard normal and that the proposed test is size and power consistent. Using our statistics, we further construct the step-down multiple comparison procedure for the simultaneous test for independence. Accuracy of the proposed tests in finite samples is shown through simulations for a variety of high-dimensional scenarios.