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Article: CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications
Title | CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications |
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Authors | |
Keywords | Central limit theorem Equality of covariance matrices Large-dimensional covariance matrices Large-dimensional Fisher matrix Linear spectral statistics |
Issue Date | 2017 |
Publisher | Bernoulli Society for Mathematical Statistics and Probability. The Journal's web site is located at http://projecteuclid.org/euclid.bj |
Citation | Bernoulli, 2017, v. 23 n. 2, p. 1130-1178 How to Cite? |
Abstract | Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two covariance matrices, or testing the independence between sub-groups of a multivariate random vector. Most of the existing work on random Fisher matrices deals with a particular situation where the population covariance matrices are equal. In this paper, we consider general Fisher matrices with arbitrary population covariance matrices and develop their spectral properties when the dimensions are proportionally large compared to the sample size. The paper has two main contributions: first the limiting distribution of the eigenvalues of a general Fisher matrix is found and second, a central limit theorem is established for a wide class of functionals of these eigenvalues. Applications of the main results are also developed for testing hypotheses on high-dimensional covariance matrices. |
Persistent Identifier | http://hdl.handle.net/10722/231309 |
ISSN | 2019 Impact Factor: 1.496 2015 SCImago Journal Rankings: 2.120 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Zheng, S | - |
dc.contributor.author | Bai, Z | - |
dc.contributor.author | Yao, JJ | - |
dc.date.accessioned | 2016-09-20T05:22:13Z | - |
dc.date.available | 2016-09-20T05:22:13Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Bernoulli, 2017, v. 23 n. 2, p. 1130-1178 | - |
dc.identifier.issn | 1350-7265 | - |
dc.identifier.uri | http://hdl.handle.net/10722/231309 | - |
dc.description.abstract | Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two covariance matrices, or testing the independence between sub-groups of a multivariate random vector. Most of the existing work on random Fisher matrices deals with a particular situation where the population covariance matrices are equal. In this paper, we consider general Fisher matrices with arbitrary population covariance matrices and develop their spectral properties when the dimensions are proportionally large compared to the sample size. The paper has two main contributions: first the limiting distribution of the eigenvalues of a general Fisher matrix is found and second, a central limit theorem is established for a wide class of functionals of these eigenvalues. Applications of the main results are also developed for testing hypotheses on high-dimensional covariance matrices. | - |
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 | Equality of covariance matrices | - |
dc.subject | Large-dimensional covariance matrices | - |
dc.subject | Large-dimensional Fisher matrix | - |
dc.subject | Linear spectral statistics | - |
dc.title | CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications | - |
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 | 10.3150/15-BEJ772 | - |
dc.identifier.scopus | eid_2-s2.0-85012893732 | - |
dc.identifier.hkuros | 263091 | - |
dc.identifier.volume | 23 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 1130 | - |
dc.identifier.epage | 1178 | - |
dc.identifier.isi | WOS:000394556600012 | - |
dc.publisher.place | Netherlands | - |
dc.identifier.issnl | 1350-7265 | - |