One-Sided Multivariate Test for Two Population Means with Common Unknown Covariance Matrices of High-Dimensional Data

Abstract

In this paper, a novel multivariate test for analyzing multivariate datasets with fewer observations than the dimension is developed. More specifically, we consider the problem of the one-sided hypothesis testing of mean vectors from two multivariate normal populations when the covariance matrices are commonly unknown. As we knew that on high-dimensional data, the sample covariance matrix is singular, a new test is proposed based on the classical Hotelling’s test and the idea of keeping more information from the sample covariance matrices as much as possible. The simulation results showed that the proposed test gave the attained significance level of the proposed test close to setting nominal significance level satisfactorily and also gave high the attained power of the test. Furthermore, the performance of the proposed test is also shown by an empirical analysis of the DNA microarray data set.