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In this paper, we consider testing the correlation coefficient matrix betweentwo subsets of high-dimensional variables. We produce a test statistic by usingthe extended cross-data-matrix (ECDM) methodology and show the unbiasedness ofECDM estimator. We also show that the ECDM estimator has the consistencyproperty and the asymptotic normality in high-dimensional settings. We proposea test procedure by the ECDM estimator and evaluate its asymptotic size andpower theoretically and numerically. We give several applications of the ECDMestimator. Finally, we demonstrate how the test procedure performs in actualdata analyses by using a microarray data set.

High-dimensional inference on covariance structures via the extended cross-data-matrix methodology