A Two-Sample Test for Mean Vectors in High-Dimensional Data

Abstract

Modern measurement technology has enabled the capture of high-dimensional data by researchers and statisticians and classical statistical inferences, such as the renowned Hotelling’s T² test, are no longer valid when the dimension of the data equals or exceeds the sample size. Importantly, when correlations among variables in a dataset exist, taking them into account in the analysis method would provide more accurate conclusions. In this article, we consider the hypothesis testing problem for two mean vectors in high-dimensional data with an underlying normality assumption. A new test is proposed based on the idea of keeping more information from the sample covariances. The asymptotic null distribution of the test statistic is derived. The simulation results show that the proposed test performs well comparing with other competing tests and becomes more powerful when the dimension increases for a given sample size. The proposed test is also illustrated with an analysis of DNA microarray data.