On the test of covariance between two high-dimensional random vectors

We consider a problem of association test in high dimension. A new test statistic is proposed based on the covariance of random vectors and its asymptotic properties are derived under both the null hypothesis and the local alternatives. Furthermore power enhancement technique is utilized to boost the empirical power especially under sparse alternatives. We examine the finite-sample performances of the proposed test via Monte Carlo simulations, which show that the proposed test outperforms some existing procedures. An empirical analysis of a microarray data is demonstrated to detect the relationship between the genes.