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

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  • Bao, Zhigang

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).

Suggested Citation

  • Bao, Zhigang, 2012. "Strong convergence of ESD for the generalized sample covariance matrices when p/n→0," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 894-901.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:894-901
    DOI: 10.1016/j.spl.2012.01.012
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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. Wang, Lili & Paul, Debashis, 2014. "Limiting spectral distribution of renormalized separable sample covariance matrices when p/n→0," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 25-52.
    2. 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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