Geodesic
The Rate of Convergence of Spectra of Sample Covariance Matrices
Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 1, pp. 202-213

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It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance matrix $p^{-1}XX^T$, where $X$ is an $n\times p$ matrix with independent entries and the distribution function of the Marchenko–Pastur law is of order $O(n^{-1/2})$. The bounds hold uniformly for any $p$, including $p/n$ equal or close to $1$.
Keywords: sample covariance matrix, spectral distribution function.
Mots-clés : Marchenko–Pastur distribution 
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F. Götze; A. N. Tikhomirov. The Rate of Convergence of Spectra of Sample Covariance Matrices. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 1, pp. 202-213. http://geodesic.mathdoc.fr/item/TVP_2009_54_1_a13/