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

Zhigang Bao

Statistics & Probability Letters, 2012, vol. 82, issue 5, 894-901

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).

Keywords: Sample covariance matrix; Stieltjes transform; Limiting spectral distribution (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2012.01.012

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