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Article: CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications

TitleCLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications
Authors
Issue Date2017
PublisherBernoulli 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?
AbstractRandom 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 Identifierhttp://hdl.handle.net/10722/231309
ISSN
2015 Impact Factor: 1.372
2015 SCImago Journal Rankings: 2.120

 

DC FieldValueLanguage
dc.contributor.authorZheng, S-
dc.contributor.authorBai, Z-
dc.contributor.authorYao, JJ-
dc.date.accessioned2016-09-20T05:22:13Z-
dc.date.available2016-09-20T05:22:13Z-
dc.date.issued2017-
dc.identifier.citationBernoulli, 2017, v. 23 n. 2, p. 1130-1178-
dc.identifier.issn1350-7265-
dc.identifier.urihttp://hdl.handle.net/10722/231309-
dc.description.abstractRandom 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.languageeng-
dc.publisherBernoulli Society for Mathematical Statistics and Probability. The Journal's web site is located at http://projecteuclid.org/euclid.bj-
dc.relation.ispartofBernoulli-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.titleCLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications-
dc.typeArticle-
dc.identifier.emailYao, JJ: jeffyao@hku.hk-
dc.identifier.authorityYao, JJ=rp01473-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.3150/15-BEJ772-
dc.identifier.hkuros263091-
dc.identifier.volume23-
dc.identifier.issue2-
dc.identifier.spage1130-
dc.identifier.epage1178-
dc.publisher.placeNetherlands-

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