Inference on high-dimensional mean vectors under the strongly spiked eigenvalue model

Abstract

In this paper, we discuss inference problems on high-dimensional mean vectors under the strongly spiked eigenvalue (SSE) model. First, we consider one-sample test. In order to avoid huge noise, we derive a new test statistic by using a data transformation technique. We show that the asymptotic normality can be established for the new test statistic. We give an asymptotic size and power of a new test procedure and investigate the performance theoretically and numerically. We apply the findings to the construction of confidence regions on the mean vector under the SSE model. We further discuss multi-sample problems under the SSE models. Finally, we demonstrate the new test procedure by using actual microarray data sets.