Statistica Sinica: Preprint
doi:10.5705/ss.202016.0063
We consider two-sample tests for high-dimensional data under two disjoint models: the
strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. We provide a
general test statistic as a function of a positive-semidefinite matrix. We give sufficient
conditions for the test statistic to hold a consistency property and the asymptotic normality.
We discuss an optimality of the test statistic under the NSSE model. We also investigate the
test statistic under the SSE model by considering strongly spiked eigenstructures and create
a new effective test procedure for the SSE model. Finally, we demonstrate the new test
procedure by using microarray data sets.