In this paper, we propose a new statistic for testing a one-sided hypothesis of mean vectors from two multivariate normal populations when the covariance matrices are unknown and unequal for high-dimensional data. As we know that the sample covariance matrix is singular for high-dimensional data, the proposed test is based on the idea of keeping as much information as possible from the sample covariance matrices. The performance of the proposed test is assessed in a simulation study with varied situations. The simulation results show that the proposed test was satisfactory in attaining nominal significance values close to set levels and the attained test power was excellent in every situation considered. Finally, the efficacy of the proposed test is illustrated with an analysis of DNA microarray data.
