Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data
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KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractWe propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods. This article is protected by copyright. All rights reserved.
CitationHu Z, Tong T, Genton MG (2018) Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data. Biometrics. Available: http://dx.doi.org/10.1111/biom.12984.
SponsorsThe authors thank the editor, the associate editor and three reviewers for their constructive comments that have led to a substantial improvement of the paper. Tiejun Tong's research was supported by the Hong Kong RGC Grant (No. HKBU12303918), the National Natural Science Foundation of China (No. 11671338), the Health and Medical Research Fund (No. 04150476), and three Hong Kong Baptist University Grants (RC-IG-FNRA/17-18/13, FRG1/17-18/045 and FRG2/17-18/020). Marc G. Genton's research was supported by the King Abdullah University of Science and Technology (KAUST).