Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data

Handle URI:
http://hdl.handle.net/10754/626484
Title:
Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data
Authors:
Hu, Zongliang; Tong, Tiejun; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
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 require the assumption that the covariance matrix follows a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and can be widely applied in practice. Finally, simulation studies and a real data analysis are also conducted to demonstrate the advantages of our likelihood ratio test method.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
27-Oct-2017
ARXIV:
arXiv:1710.09982
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1710.09982v1; http://arxiv.org/pdf/1710.09982v1
Appears in Collections:
Other/General Submission; Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHu, Zongliangen
dc.contributor.authorTong, Tiejunen
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2017-12-28T07:32:12Z-
dc.date.available2017-12-28T07:32:12Z-
dc.date.issued2017-10-27en
dc.identifier.urihttp://hdl.handle.net/10754/626484-
dc.description.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 require the assumption that the covariance matrix follows a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and can be widely applied in practice. Finally, simulation studies and a real data analysis are also conducted to demonstrate the advantages of our likelihood ratio test method.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1710.09982v1en
dc.relation.urlhttp://arxiv.org/pdf/1710.09982v1en
dc.rightsArchived with thanks to arXiven
dc.titleDiagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Dataen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Mathematics, Hong Kong Baptist University, Hong Kongen
dc.identifier.arxividarXiv:1710.09982en
kaust.authorGenton, Marc G.en
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