Please use this identifier to cite or link to this item: https://doi.org/10.1214/EJP.v17-1962
Title: Tracy-Widom law for the extreme eigenvalues of sample correlation matrices
Authors: Bao, Z.
Pan, G.
Zhou, W. 
Keywords: Extreme eigenvalues
Sample correlation matrices
Sample covariance matrices
Stieltjes transform
Tracy-Widom law
Issue Date: 2012
Citation: Bao, 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
Abstract: Let 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.
Source Title: Electronic Journal of Probability
URI: http://scholarbank.nus.edu.sg/handle/10635/105441
ISSN: 10836489
DOI: 10.1214/EJP.v17-1962
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