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Article: Strong convergence of ESD for the generalized sample covariance matrices when p/n→0
Title | Strong convergence of ESD for the generalized sample covariance matrices when p/n→0 |
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Authors | |
Keywords | Limiting spectral distribution Sample covariance matrix Stieltjes transform |
Issue Date | 2012 |
Citation | Statistics and Probability Letters, 2012, v. 82, n. 5, p. 894-901 How to Cite? |
Abstract | Let X=[X ij]p×n be a p× n random matrix whose entries are i.i.d real random variables satisfying the moment condition E{double-struck}X 114<∞. Let T be a p× p deterministic nonnegative definite matrix. It is assumed that the empirical distribution of the eigenvalues of T converges weakly to a probability distribution. We consider the renormalized sample covariance matrix H̃=√n/p(1/nT 1/2XX tT 1/2-T) in the case of p/n→ 0 as p, n→ ∞. We study the limiting spectral distribution of H in this paper. The limiting distribution is shown to be coincident with the case of a generalized Wigner matrix considered in. Bai and Zhang (2010). © 2012 Elsevier B.V.. |
Persistent Identifier | http://hdl.handle.net/10722/348961 |
ISSN | 2023 Impact Factor: 0.9 2023 SCImago Journal Rankings: 0.448 |
DC Field | Value | Language |
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dc.contributor.author | Bao, Zhigang | - |
dc.date.accessioned | 2024-10-17T06:55:13Z | - |
dc.date.available | 2024-10-17T06:55:13Z | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | Statistics and Probability Letters, 2012, v. 82, n. 5, p. 894-901 | - |
dc.identifier.issn | 0167-7152 | - |
dc.identifier.uri | http://hdl.handle.net/10722/348961 | - |
dc.description.abstract | Let X=[X ij]p×n be a p× n random matrix whose entries are i.i.d real random variables satisfying the moment condition E{double-struck}X 114<∞. Let T be a p× p deterministic nonnegative definite matrix. It is assumed that the empirical distribution of the eigenvalues of T converges weakly to a probability distribution. We consider the renormalized sample covariance matrix H̃=√n/p(1/nT 1/2XX tT 1/2-T) in the case of p/n→ 0 as p, n→ ∞. We study the limiting spectral distribution of H in this paper. The limiting distribution is shown to be coincident with the case of a generalized Wigner matrix considered in. Bai and Zhang (2010). © 2012 Elsevier B.V.. | - |
dc.language | eng | - |
dc.relation.ispartof | Statistics and Probability Letters | - |
dc.subject | Limiting spectral distribution | - |
dc.subject | Sample covariance matrix | - |
dc.subject | Stieltjes transform | - |
dc.title | Strong convergence of ESD for the generalized sample covariance matrices when p/n→0 | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.spl.2012.01.012 | - |
dc.identifier.scopus | eid_2-s2.0-84857251607 | - |
dc.identifier.volume | 82 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 894 | - |
dc.identifier.epage | 901 | - |