File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Corrections to LRT on large-dimensional covariance matrix by RMT

TitleCorrections to LRT on large-dimensional covariance matrix by RMT
Authors
KeywordsHigh-dimensional data
Marčenko-pastur distributions
Random F-matrices
Testing on covariance matrices
Issue Date2009
PublisherInstitute of Mathematical Statistics
Citation
Annals Of Statistics, 2009, v. 37 n. 6 B, p. 3822-3840 How to Cite?
AbstractIn this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension p is large compared to the sample size n. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose necessary corrections for these LR tests to cope with high-dimensional effects. The asymptotic distributions of these corrected tests under the null are given. Simulations demonstrate that the corrected LR tests yield a realized size close to nominal level for both moderate p (around 20) and high dimension, while the traditional LR tests with χ 2 approximation fails. Another contribution from the paper is that for testing the equality between two covariance matrices, the proposed correction applies equally for non-Gaussian populations yielding a valid pseudo-likelihood ratio test. © Institute of Mathematical Statistics, 2009.
Persistent Identifierhttp://hdl.handle.net/10722/132605
ISSN
2015 Impact Factor: 2.78
2015 SCImago Journal Rankings: 6.653
References

 

DC FieldValueLanguage
dc.contributor.authorBai, Zen_HK
dc.contributor.authorJiang, Den_HK
dc.contributor.authorYao, JFen_HK
dc.contributor.authorZheng, Sen_HK
dc.date.accessioned2011-03-28T09:26:57Z-
dc.date.available2011-03-28T09:26:57Z-
dc.date.issued2009en_HK
dc.identifier.citationAnnals Of Statistics, 2009, v. 37 n. 6 B, p. 3822-3840en_HK
dc.identifier.issn0090-5364en_HK
dc.identifier.urihttp://hdl.handle.net/10722/132605-
dc.description.abstractIn this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension p is large compared to the sample size n. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose necessary corrections for these LR tests to cope with high-dimensional effects. The asymptotic distributions of these corrected tests under the null are given. Simulations demonstrate that the corrected LR tests yield a realized size close to nominal level for both moderate p (around 20) and high dimension, while the traditional LR tests with χ 2 approximation fails. Another contribution from the paper is that for testing the equality between two covariance matrices, the proposed correction applies equally for non-Gaussian populations yielding a valid pseudo-likelihood ratio test. © Institute of Mathematical Statistics, 2009.en_HK
dc.languageengen_US
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.ispartofAnnals of Statisticsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectHigh-dimensional dataen_HK
dc.subjectMarčenko-pastur distributionsen_HK
dc.subjectRandom F-matricesen_HK
dc.subjectTesting on covariance matricesen_HK
dc.titleCorrections to LRT on large-dimensional covariance matrix by RMTen_HK
dc.typeArticleen_HK
dc.identifier.emailYao, JF: jeffyao@hku.hken_HK
dc.identifier.authorityYao, JF=rp01473en_HK
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1214/09-AOS694en_HK
dc.identifier.scopuseid_2-s2.0-73949135723en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-73949135723&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume37en_HK
dc.identifier.issue6 Ben_HK
dc.identifier.spage3822en_HK
dc.identifier.epage3840en_HK
dc.identifier.eissn2168-8966-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridBai, Z=7202524223en_HK
dc.identifier.scopusauthoridJiang, D=35299477800en_HK
dc.identifier.scopusauthoridYao, JF=7403503451en_HK
dc.identifier.scopusauthoridZheng, S=7403146780en_HK
dc.customcontrol.immutablecsl 140409-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats