Two-Sample Test of High Dimensional Means under Dependency
Tony Cai, Weidong Liu, and Yin Xia
This paper considers in the high dimensional setting a canonical testing problem in multivariate analysis, namely testing the equality of two mean vectors. We introduce a new test statistic that is based on a linear transformation of the data by the precision matrix which incorporates the correlations among the variables. Limiting null distribution of the test statistic and the power of the test are analyzed. It is shown that the test is particularly powerful against sparse alternatives and enjoys certain optimality. A simulation study is carried out to examine the numerical performance of the test and compare with other tests given in the literature. The results show that the proposed test significantly outperforms those tests in a range of settings.