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Article: On eigenvalues of a high-dimensional spatial-sign covariance matrix
Title | On eigenvalues of a high-dimensional spatial-sign covariance matrix |
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Authors | |
Keywords | central limit theorem eigenvalue distribution Linear spectral statistics spatial-sign covariance matrix |
Issue Date | 2022 |
Publisher | Bernoulli Society for Mathematical Statistics and Probability. The Journal's web site is located at http://projecteuclid.org/euclid.bj |
Citation | Bernoulli, 2022, v. 28 n. 1, p. 606-637 How to Cite? |
Abstract | This paper investigates limiting spectral properties of a high-dimensional sample spatial-sign covariance matrix when both the dimension of the observations and the sample size grow to infinity. The underlying population is general enough to include the popular independent components model and the family of elliptical distributions. The first result of the paper shows that the empirical spectral distribution of a high dimensional sample spatial-sign covariance matrix converges to a generalized Marčenko-Pastur distribution. Secondly, a new central limit theorem for a class of related linear spectral statistics is established. |
Persistent Identifier | http://hdl.handle.net/10722/310527 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.522 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Li, W | - |
dc.contributor.author | Wang, Q | - |
dc.contributor.author | Yao, JJ | - |
dc.contributor.author | Zhou, W | - |
dc.date.accessioned | 2022-02-07T07:57:58Z | - |
dc.date.available | 2022-02-07T07:57:58Z | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | Bernoulli, 2022, v. 28 n. 1, p. 606-637 | - |
dc.identifier.issn | 1350-7265 | - |
dc.identifier.uri | http://hdl.handle.net/10722/310527 | - |
dc.description.abstract | This paper investigates limiting spectral properties of a high-dimensional sample spatial-sign covariance matrix when both the dimension of the observations and the sample size grow to infinity. The underlying population is general enough to include the popular independent components model and the family of elliptical distributions. The first result of the paper shows that the empirical spectral distribution of a high dimensional sample spatial-sign covariance matrix converges to a generalized Marčenko-Pastur distribution. Secondly, a new central limit theorem for a class of related linear spectral statistics is established. | - |
dc.language | eng | - |
dc.publisher | Bernoulli Society for Mathematical Statistics and Probability. The Journal's web site is located at http://projecteuclid.org/euclid.bj | - |
dc.relation.ispartof | Bernoulli | - |
dc.subject | central limit theorem | - |
dc.subject | eigenvalue distribution | - |
dc.subject | Linear spectral statistics | - |
dc.subject | spatial-sign covariance matrix | - |
dc.title | On eigenvalues of a high-dimensional spatial-sign covariance matrix | - |
dc.type | Article | - |
dc.identifier.email | Yao, JJ: jeffyao@hku.hk | - |
dc.identifier.authority | Yao, JJ=rp01473 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.3150/21-BEJ1360 | - |
dc.identifier.scopus | eid_2-s2.0-85120377213 | - |
dc.identifier.hkuros | 331633 | - |
dc.identifier.volume | 28 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 606 | - |
dc.identifier.epage | 637 | - |
dc.identifier.isi | WOS:000766621400002 | - |
dc.publisher.place | Netherlands | - |