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Strong convergence of ESD for the generalized sample covariance matrices when p/n→0

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  • Bao, Zhigang
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    Abstract

    Let X=[Xij]p×n be a p×n random matrix whose entries are i.i.d real random variables satisfying the moment condition EX114<∞. Let T be a p×p deterministic nonnegative definite matrix. It is assumed that the empirical distribution of the eigenvalues of T converges weakly to a probability distribution. We consider the renormalized sample covariance matrix H̃=np(1nT1/2XXtT1/2−T) in the case of p/n→0 as p,n→∞. We study the limiting spectral distribution of H̃ in this paper. The limiting distribution is shown to be coincident with the case of a generalized Wigner matrix considered in Bai and Zhang (2010).

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 5 ()
    Pages: 894-901

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:894-901

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    Related research

    Keywords: Sample covariance matrix; Stieltjes transform; Limiting spectral distribution;

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    1. Bai, Z.D. & Zhang, L.X., 2010. "The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1927-1949, October.
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    Cited by:
    1. Xie, Junshan, 2013. "Limiting spectral distribution of normalized sample covariance matrices with p/n→0," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 543-550.

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