Please use this identifier to cite or link to this item: https://doi.org/10.1214/EJP.v17-1962
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dc.titleTracy-Widom law for the extreme eigenvalues of sample correlation matrices
dc.contributor.authorBao, Z.
dc.contributor.authorPan, G.
dc.contributor.authorZhou, W.
dc.date.accessioned2014-10-28T05:16:17Z
dc.date.available2014-10-28T05:16:17Z
dc.date.issued2012
dc.identifier.citationBao, Z., Pan, G., Zhou, W. (2012). Tracy-Widom law for the extreme eigenvalues of sample correlation matrices. Electronic Journal of Probability 17 : -. ScholarBank@NUS Repository. https://doi.org/10.1214/EJP.v17-1962
dc.identifier.issn10836489
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/105441
dc.description.abstractLet the sample correlation matrix be W = YY Twhere Y = (y ij) p;n with y ij. We assume to be a collection of independent symmetrically distributed random variables with sub-exponential tails. Moreover, for any i, we assume x ij, 1 ≤ j ≤ n to be identically distributed. We assume 0 < p < n and p=n → y with some y ε (0; 1) as p; n → ∞. In this paper, we provide the Tracy-Widom law (TW1) for both the largest and smallest eigenvalues of W. If x ij are i.i.d. standard normal, we can derive the TW 1 for both the largest and smallest eigenvalues of the matrix R = RR T, where R = (r ij) p;n with r ij.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1214/EJP.v17-1962
dc.sourceScopus
dc.subjectExtreme eigenvalues
dc.subjectSample correlation matrices
dc.subjectSample covariance matrices
dc.subjectStieltjes transform
dc.subjectTracy-Widom law
dc.typeArticle
dc.contributor.departmentSTATISTICS & APPLIED PROBABILITY
dc.description.doi10.1214/EJP.v17-1962
dc.description.sourcetitleElectronic Journal of Probability
dc.description.volume17
dc.description.page-
dc.identifier.isiut000309961200001
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