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Article: Joint Central Limit Theorem for Eigenvalue Statistics from Several Dependent Large Dimensional Sample Covariance Matrices with Application

TitleJoint Central Limit Theorem for Eigenvalue Statistics from Several Dependent Large Dimensional Sample Covariance Matrices with Application
Authors
Keywordscentral limit theorem
high‐dimensional times series
large sample covariance matrices
linear spectral statistics
white noise test
Issue Date2018
PublisherWiley-Blackwell Publishing Ltd..
Citation
Scandinavian Journal of Statistics, 2018, v. 45 n. 3, p. 699-728 How to Cite?
AbstractLet Xn = (xij) be a k×n data matrix with complex‐valued, independent and standardized entries satisfying a Lindeberg‐type moment condition. We consider simultaneously R sample covariance matrices urn:x-wiley:sjos:media:sjos12320:sjos12320-math-0001, where the Qr's are non‐random real matrices with common dimensions p×k(k≥p). Assuming that both the dimension p and the sample size n grow to infinity, the limiting distributions of the eigenvalues of the matrices {Bnr} are identified, and as the main result of the paper, we establish a joint central limit theorem (CLT) for linear spectral statistics of the R matrices {Bnr}. Next, this new CLT is applied to the problem of testing a high‐dimensional white noise in time series modelling. In experiments, the derived test has a controlled size and is significantly faster than the classical permutation test, although it does have lower power. This application highlights the necessity of such joint CLT in the presence of several dependent sample covariance matrices. In contrast, all the existing works on CLT for linear spectral statistics of large sample covariance matrices deal with a single sample covariance matrix (R = 1).
Persistent Identifierhttp://hdl.handle.net/10722/259518
ISSN
2015 Impact Factor: 0.908
2015 SCImago Journal Rankings: 1.362

 

DC FieldValueLanguage
dc.contributor.authorLi, WM-
dc.contributor.authorLi, Z-
dc.contributor.authorYao, JJ-
dc.date.accessioned2018-09-03T04:09:11Z-
dc.date.available2018-09-03T04:09:11Z-
dc.date.issued2018-
dc.identifier.citationScandinavian Journal of Statistics, 2018, v. 45 n. 3, p. 699-728-
dc.identifier.issn0303-6898-
dc.identifier.urihttp://hdl.handle.net/10722/259518-
dc.description.abstractLet Xn = (xij) be a k×n data matrix with complex‐valued, independent and standardized entries satisfying a Lindeberg‐type moment condition. We consider simultaneously R sample covariance matrices urn:x-wiley:sjos:media:sjos12320:sjos12320-math-0001, where the Qr's are non‐random real matrices with common dimensions p×k(k≥p). Assuming that both the dimension p and the sample size n grow to infinity, the limiting distributions of the eigenvalues of the matrices {Bnr} are identified, and as the main result of the paper, we establish a joint central limit theorem (CLT) for linear spectral statistics of the R matrices {Bnr}. Next, this new CLT is applied to the problem of testing a high‐dimensional white noise in time series modelling. In experiments, the derived test has a controlled size and is significantly faster than the classical permutation test, although it does have lower power. This application highlights the necessity of such joint CLT in the presence of several dependent sample covariance matrices. In contrast, all the existing works on CLT for linear spectral statistics of large sample covariance matrices deal with a single sample covariance matrix (R = 1).-
dc.languageeng-
dc.publisherWiley-Blackwell Publishing Ltd.. -
dc.relation.ispartofScandinavian Journal of Statistics-
dc.rightsPreprint This is the pre-peer reviewed version of the following article: [FULL CITE], which has been published in final form at [Link to final article]. Authors are not required to remove preprints posted prior to acceptance of the submitted version. Postprint This is the accepted version of the following article: [full citation], which has been published in final form at [Link to final article]. -
dc.subjectcentral limit theorem-
dc.subjecthigh‐dimensional times series-
dc.subjectlarge sample covariance matrices-
dc.subjectlinear spectral statistics-
dc.subjectwhite noise test-
dc.titleJoint Central Limit Theorem for Eigenvalue Statistics from Several Dependent Large Dimensional Sample Covariance Matrices with Application-
dc.typeArticle-
dc.identifier.emailYao, JJ: jeffyao@hku.hk-
dc.identifier.authorityYao, JJ=rp01473-
dc.identifier.doi10.1111/sjos.12320-
dc.identifier.hkuros289692-
dc.identifier.volume45-
dc.identifier.issue3-
dc.identifier.spage699-
dc.identifier.epage728-
dc.publisher.placeUnited Kingdom-

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