Two-Sample Test of High-Dimensional Means Under Dependency

• Activity Number: 585
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yin Xia*+ and Tony Cai and Weidong Liu
• Companies: UNC Chapel Hill and University of Pennsylvania and Shanghai Jiao Tong University
• Keywords: Extreme value distribution ; high dimensional test ; limiting null distribution ; precision matrix ; testing equality of mean vectors ; hypothesis testing

Abstract

This talk considers in the high dimensional setting a canonical testing problem in multivariate analysis, namely testing the equality of two mean vectors. The focus is on the construction of a test that is particularly well suited for testing against sparse alternatives. 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, both for the case the precision matrix is known and the case it is unknown, 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 numerical results show that the proposed test signicantly outperforms those tests against sparse alternatives.