Testing identity of high-dimensional covariance matrix

Two new statistics are proposed for testing the identity of high-dimensional covariance matrix. Applying the large dimensional random matrix theory, we study the asymptotic distributions of our proposed statistics under the situation that the dimension p and the sample size n tend to infinity proportionally. The proposed tests can accommodate the situation that the data dimension is much larger than the sample size, and the situation that the population distribution is non-Gaussian. The numerical studies demonstrate that the proposed tests have good performance on the empirical powers for a wide range of dimensions and sample sizes.