A High-Dimensional Two-Sample Test for Non-Gaussian Data under a Strongly Spiked Eigenvalue Model

Abstract

In this paper, we discuss two-sample tests for high-dimension, non-Gaussian data. We suppose that two classes have a strongly spiked eigenvalue model. First, we investigate the noise space for high-dimension, non-Gaussian data. A two-sample test is proposed by using the cross-data-matrix (CDM) methodology and its power is derived under some regularity conditions when the dimension is very large. We discuss the validity of assumptions. We check the performance of the proposed two-sample test procedure by simulations. Finally, we demonstrate the proposed two-sample test in actual data analyses.