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Article: On structure testing for component covariance matrices of a high dimensional mixture

TitleOn structure testing for component covariance matrices of a high dimensional mixture
Authors
KeywordsLarge covariance matrix
Marčenko–Pastur law
Sphericity test
Issue Date2018
PublisherWiley-Blackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/RSSB
Citation
Journal of the Royal Statistical Society. Series B: Statistical Methodology, 2018, v. 80 n. 2, p. 293-318 How to Cite?
AbstractBy studying the family of p‐dimensional scale mixtures, the paper shows for the first time a non‐trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated Marčenko–Pastur law. A different and new limit is found and characterized. The reasons for failure of the Marčenko–Pastur limit in this situation are found to be a strong dependence between the p‐co‐ordinates of the mixture. Next, we address the problem of testing whether the mixture has a spherical covariance matrix. To analyse the traditional John's‐type test we establish a novel and general central limit theorem for linear statistics of eigenvalues of the sample covariance matrix. It is shown that John's test and its recent high dimensional extensions both fail for high dimensional mixtures, precisely because of the different spectral limit above. As a remedy, a new test procedure is constructed afterwards for the sphericity hypothesis. This test is then applied to identify the covariance structure in model‐based clustering. It is shown that the test has much higher power than the widely used integrated classification likelihood and Bayesian information criteria in detecting non‐spherical component covariance matrices of a high dimensional mixture.
Persistent Identifierhttp://hdl.handle.net/10722/259514
ISSN
2023 Impact Factor: 3.1
2023 SCImago Journal Rankings: 4.330
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLi, WM-
dc.contributor.authorYao, JJ-
dc.date.accessioned2018-09-03T04:09:06Z-
dc.date.available2018-09-03T04:09:06Z-
dc.date.issued2018-
dc.identifier.citationJournal of the Royal Statistical Society. Series B: Statistical Methodology, 2018, v. 80 n. 2, p. 293-318-
dc.identifier.issn1369-7412-
dc.identifier.urihttp://hdl.handle.net/10722/259514-
dc.description.abstractBy studying the family of p‐dimensional scale mixtures, the paper shows for the first time a non‐trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated Marčenko–Pastur law. A different and new limit is found and characterized. The reasons for failure of the Marčenko–Pastur limit in this situation are found to be a strong dependence between the p‐co‐ordinates of the mixture. Next, we address the problem of testing whether the mixture has a spherical covariance matrix. To analyse the traditional John's‐type test we establish a novel and general central limit theorem for linear statistics of eigenvalues of the sample covariance matrix. It is shown that John's test and its recent high dimensional extensions both fail for high dimensional mixtures, precisely because of the different spectral limit above. As a remedy, a new test procedure is constructed afterwards for the sphericity hypothesis. This test is then applied to identify the covariance structure in model‐based clustering. It is shown that the test has much higher power than the widely used integrated classification likelihood and Bayesian information criteria in detecting non‐spherical component covariance matrices of a high dimensional mixture.-
dc.languageeng-
dc.publisherWiley-Blackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/RSSB-
dc.relation.ispartofJournal of the Royal Statistical Society. Series B: Statistical Methodology-
dc.rightsPreprint This is the pre-peer reviewed version of the following article: [FULL CITE], which has been published in final form at [Link to final article]. Authors are not required to remove preprints posted prior to acceptance of the submitted version. Postprint This is the accepted version of the following article: [full citation], which has been published in final form at [Link to final article]. -
dc.subjectLarge covariance matrix-
dc.subjectMarčenko–Pastur law-
dc.subjectSphericity test-
dc.titleOn structure testing for component covariance matrices of a high dimensional mixture-
dc.typeArticle-
dc.identifier.emailYao, JJ: jeffyao@hku.hk-
dc.identifier.authorityYao, JJ=rp01473-
dc.identifier.doi10.1111/rssb.12248-
dc.identifier.scopuseid_2-s2.0-85041086294-
dc.identifier.hkuros289685-
dc.identifier.volume80-
dc.identifier.issue2-
dc.identifier.spage293-
dc.identifier.epage318-
dc.identifier.isiWOS:000423371000002-
dc.publisher.placeUnited Kingdom-
dc.identifier.issnl1369-7412-

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