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

Tests of the correlation matrix between two subsets of a high-dimensional random vector are considered. The test statistic is based on the extended cross-data-matrix methodology (ECDM) and shown to be unbiased. The ECDM estimator is also proved to be consistent and asymptotically Normal in high-dimensional settings. The authors propose a test procedure based on the ECDM estimator and evaluate its size and power, both theoretically and numerically. They give several applications of the ECDM estimator and illustrate the performance of the test procedure using microarray data.