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Diagonal likelihood ratio test for equality of mean vectors in high‐dimensional data
Author(s) -
Hu Zongliang,
Tong Tiejun,
Genton Marc G.
Publication year - 2019
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12984
Subject(s) - mathematics , likelihood ratio test , statistics , diagonal , covariance matrix , covariance , statistical hypothesis testing , normality , estimation of covariance matrices , matrix (chemical analysis) , chi square test , score test , materials science , geometry , composite material
We 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.