Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 76, Issue 2, Pages 349-372Publisher
WILEY-BLACKWELL
DOI: 10.1111/rssb.12034
Keywords
Covariance matrix; Extreme value distribution; High dimensional test; Hypothesis testing; Limiting null distribution; Power; Precision matrix; Testing equality of mean vectors
Categories
Funding
- National Science Foundation Focused Research Group [DMS-0854973]
- National Natural Science Foundation of China [11201298]
- Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning
- 'Foundation for the author of national excellent doctoral dissertation of PR China'
- Shanghai Jiao Tong University, People's Republic of China
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1208982] Funding Source: National Science Foundation
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The 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 between the variables. The limiting null distribution of the test statistic and the power of the test are analysed. 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 to compare it with other tests given in the literature. The results show that the test proposed significantly outperforms those tests in a range of settings.
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