Equality tests of high-dimensional covariance matrices under the strongly spiked eigenvalue model

We consider the equality test of high-dimensional covariance matrices under the strongly spiked eigenvalue (SSE) model. We find the difference of covariance matrices by dividing high-dimensional eigenspaces into the first eigenspace and the others. We create a new test procedure on the basis of those high-dimensional eigenstructures. We precisely study the influence of spiked eigenvalues on a test statistic and consider its bias correction so that the proposed test procedure has a consistency property for the size. We also show that the proposed test procedure has preferable properties for the power. We discuss the performance of the test procedure by simulations. We give a demonstration in actual data analyses using microarray data sets