  In this paper, we consider testing the correlation coefficient matrix between
two subsets of high-dimensional variables. We produce a test statistic by using
the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of
ECDM estimator. We also show that the ECDM estimator has the consistency
property and the asymptotic normality in high-dimensional settings. We propose
a test procedure by the ECDM estimator and evaluate its asymptotic size and
power theoretically and numerically. We give several applications of the ECDM
estimator. Finally, we demonstrate how the test procedure performs in actual
data analyses by using a microarray data set.
