Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory

This paper addresses the issue of testing sphericity and identity high-dimensional population covariance matrix when data dimension exceeds sample size. The central limit theorem first four moments eigenvalues is derived using random theory for generally distributed populations. Further, some desirable asymptotic properties proposed test statistics are provided under null hypothesis as size both tend to infinity. Simulations show that tests have a greater power than existing methods spiked model.