On asymptotic expansion and CLT of linear eigenvalue statistics for sample covariance matrices when N/M→0

2011/04/18 by Bao, Zhigang
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1104.3470

Abstract

We study the renormalized real sample covariance matrix H=X^TX/√(MN)-√(M/N) with N/M→0 as N, M→ ∞ in this paper. And we always assume M=M(N). Here X=[X_jk]_{M× N} is an M× N real random matrix with i.i.d entries, and we assume 𝔼|X₁₁|^5+δ

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