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Article: On the sphericity test with large-dimensional observations

TitleOn the sphericity test with large-dimensional observations
Authors
Issue Date2013
PublisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/ejs
Citation
Electronic Journal of Statistics, 2013, v. 7, p. 2164–2192 How to Cite?
AbstractIn this paper, we propose corrections to the likelihood ratio test and John’s test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with general fourth moments are first established. Using these formulas, we derive the asymptotic distribution of the two proposed test statistics under the null. These asymptotics are valid for general population, i.e. not necessarily Gaussian, provided a finite fourth-moment. Extensive Monte-Carlo experiments are conducted to assess the quality of these tests with a comparison to several existing methods from the literature. Moreover, we also obtain their asymptotic power functions under the alternative of a spiked population model as a specific alternative.
Persistent Identifierhttp://hdl.handle.net/10722/189449
ISSN
2015 Impact Factor: 0.736
2015 SCImago Journal Rankings: 1.661
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorWang, Qen_US
dc.contributor.authorYao, Jen_US
dc.date.accessioned2013-09-17T14:41:47Z-
dc.date.available2013-09-17T14:41:47Z-
dc.date.issued2013-
dc.identifier.citationElectronic Journal of Statistics, 2013, v. 7, p. 2164–2192en_US
dc.identifier.issn1935-7524-
dc.identifier.urihttp://hdl.handle.net/10722/189449-
dc.description.abstractIn this paper, we propose corrections to the likelihood ratio test and John’s test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with general fourth moments are first established. Using these formulas, we derive the asymptotic distribution of the two proposed test statistics under the null. These asymptotics are valid for general population, i.e. not necessarily Gaussian, provided a finite fourth-moment. Extensive Monte-Carlo experiments are conducted to assess the quality of these tests with a comparison to several existing methods from the literature. Moreover, we also obtain their asymptotic power functions under the alternative of a spiked population model as a specific alternative.-
dc.languageengen_US
dc.publisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/ejs-
dc.relation.ispartofElectronic Journal of Statisticsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleOn the sphericity test with large-dimensional observationsen_US
dc.typeArticleen_US
dc.identifier.emailYao, J: jeffyao@hku.hken_US
dc.identifier.authorityYao, JJ=rp01473en_US
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1214/13-EJS842-
dc.identifier.hkuros221517en_US
dc.identifier.volume7-
dc.identifier.spage2164–2192-
dc.identifier.epage2164–2192-
dc.identifier.isiWOS:000324090100001-
dc.publisher.placeUnited States-
dc.customcontrol.immutablecsl 140409-

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