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Article: Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models
Title | Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models |
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Authors | |
Keywords | Central limit theorem Extreme eigenvalues Extreme eigenvectors Joint distribution Large-dimensional sample covariance matrices Random quadratic form Random sesqulinear form Spiked population model |
Issue Date | 2014 |
Publisher | Institute 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? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/217227 |
ISSN | 2023 Impact Factor: 1.3 2023 SCImago Journal Rankings: 1.419 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Wang, Q | - |
dc.contributor.author | Su, Z | - |
dc.contributor.author | Yao, J | - |
dc.date.accessioned | 2015-09-18T05:52:48Z | - |
dc.date.available | 2015-09-18T05:52:48Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Electronic Journal of Probability, 2014, v. 19, article no. 103, p. 1-28 | - |
dc.identifier.issn | 1083-6489 | - |
dc.identifier.uri | http://hdl.handle.net/10722/217227 | - |
dc.description.abstract | In 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.language | eng | - |
dc.publisher | Institute of Mathematical Statistics. The Journal's web site is located at http://www.math.washington.edu/~ejpecp/ | - |
dc.relation.ispartof | Electronic Journal of Probability | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Central limit theorem | - |
dc.subject | Extreme eigenvalues | - |
dc.subject | Extreme eigenvectors | - |
dc.subject | Joint distribution | - |
dc.subject | Large-dimensional sample covariance matrices | - |
dc.subject | Random quadratic form | - |
dc.subject | Random sesqulinear form | - |
dc.subject | Spiked population model | - |
dc.title | Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models | - |
dc.type | Article | - |
dc.identifier.email | Yao, J: jeffyao@hku.hk | - |
dc.identifier.authority | Yao, J=rp01473 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1214/EJP.v19-3339 | - |
dc.identifier.scopus | eid_2-s2.0-84924816238 | - |
dc.identifier.hkuros | 253938 | - |
dc.identifier.volume | 19 | - |
dc.identifier.issue | 103 | - |
dc.identifier.spage | article no. 103, p. 1 | - |
dc.identifier.epage | article no. 103, p. 28 | - |
dc.identifier.isi | WOS:000348761300001 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 1083-6489 | - |