High-dimensional Two-sample Test Procedures under the Strongly Spiked Eigenvalue Model

Abstract

In this paper, we consider the two-sample test for high-dimensional data. In the high-dimensional statistical analysis, it is crucial to construct theories and methodologies depending onthe high-dimensional covariance structure. In particular, the high-dimensional noise has harmful effects upon the theory and methodology quite severely. In order to overcome the difficulty, the key is how to handle the high-dimensional spiked noise. In this paper, we deal with a typical high-dimensional noise model called the uni-SSE (strongly spiked eigenvalue)model. We propose a new test procedure that can be established without assuming the equality of the first eigenspacesbetween two classes. We show that the proposed test procedure enjoys consistency properties both for the size and power asymptoticallywhen the dimension goes to infinity while the sample sizes are fixed. We check the performance of the proposed test procedure by numerical simulations. Finally, we give a demonstration using microarray data sets and explain how to select a suitable test procedure.