Robust tests of the equality of two high-dimensional covariance matrices

It is of great importance in both theory and application to test the equality of two covariance matrices Σ1 and Σ2. This article proposes a new robust test based on spatial sign statistic regarding H0:Σ1=Σ2 in high-dimensional setting, and shows that the test statistic is asymptotically normal under elliptical distribution. Besides theoretical properties, simulation results also show that the new test significantly outperforms existing methods in terms of size and power for non normal and high-dimensional data. Analysis of colon cancer data set is carried out to demonstrate the application of the testing procedure.