A robust test for sphericity of high-dimensional covariance matrices

This paper discusses the problem of testing the sphericity of a covariance matrix in high-dimensional frameworks. A new test procedure is put forward by taking the maximum of two existing statistics which are proved weakly independent in our settings. Asymptotic distribution of the new statistic is derived for generally distributed population with a finite fourth moment. Extensive simulations demonstrate that the proposed test has a great improvement in robustness of power against various models under the alternative hypothesis.