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Article: Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models

TitleJoint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models
Authors
KeywordsCentral limit theorem
Extreme eigenvalues
Extreme eigenvectors
Joint distribution
Large-dimensional sample covariance matrices
Random quadratic form
Random sesqulinear form
Spiked population model
Issue Date2014
PublisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.math.washington.edu/~ejpecp/
Citation
Electronic Journal of Probability, 2014, v. 19, article no. 103, p. 1-28 How to Cite?
AbstractIn this paper, we derive a joint central limit theorem for random vector whose components are function of random sesquilinear forms. This result is a natural extension of the existing central limit theory on random quadratic forms. We also provide applications in random matrix theory related to large-dimensional spiked population models. For the first application, we find the joint distribution of grouped extreme sample eigenvalues correspond to the spikes. And for the second application, under the assumption that the population covariance matrix is diagonal with k (fixed) simple spikes, we derive the asymptotic joint distribution of the extreme sample eigenvalue and its corresponding sample eigenvector projection.
Persistent Identifierhttp://hdl.handle.net/10722/217227
ISSN
2019 Impact Factor: 1.123
2015 SCImago Journal Rankings: 1.554
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorWang, Q-
dc.contributor.authorSu, Z-
dc.contributor.authorYao, J-
dc.date.accessioned2015-09-18T05:52:48Z-
dc.date.available2015-09-18T05:52:48Z-
dc.date.issued2014-
dc.identifier.citationElectronic Journal of Probability, 2014, v. 19, article no. 103, p. 1-28-
dc.identifier.issn1083-6489-
dc.identifier.urihttp://hdl.handle.net/10722/217227-
dc.description.abstractIn this paper, we derive a joint central limit theorem for random vector whose components are function of random sesquilinear forms. This result is a natural extension of the existing central limit theory on random quadratic forms. We also provide applications in random matrix theory related to large-dimensional spiked population models. For the first application, we find the joint distribution of grouped extreme sample eigenvalues correspond to the spikes. And for the second application, under the assumption that the population covariance matrix is diagonal with k (fixed) simple spikes, we derive the asymptotic joint distribution of the extreme sample eigenvalue and its corresponding sample eigenvector projection.-
dc.languageeng-
dc.publisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.math.washington.edu/~ejpecp/-
dc.relation.ispartofElectronic Journal of Probability-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectCentral limit theorem-
dc.subjectExtreme eigenvalues-
dc.subjectExtreme eigenvectors-
dc.subjectJoint distribution-
dc.subjectLarge-dimensional sample covariance matrices-
dc.subjectRandom quadratic form-
dc.subjectRandom sesqulinear form-
dc.subjectSpiked population model-
dc.titleJoint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models-
dc.typeArticle-
dc.identifier.emailYao, J: jeffyao@hku.hk-
dc.identifier.authorityYao, J=rp01473-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1214/EJP.v19-3339-
dc.identifier.scopuseid_2-s2.0-84924816238-
dc.identifier.hkuros253938-
dc.identifier.volume19-
dc.identifier.issue103-
dc.identifier.spagearticle no. 103, p. 1-
dc.identifier.epagearticle no. 103, p. 28-
dc.identifier.isiWOS:000348761300001-
dc.publisher.placeUnited States-

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