The rate of convergence of spectra of sample covariance matrices

Details The rate of convergence of spectra of sample covariance matrices The rate of convergence of spectra of sample covariance matrices

2007-12-21

arxiv.org/abs/0712.3725v1

Mathematics

Probability

Scientific paper

It is shown that the Kolmogorov distance between the spectral distribution
function of a random covariance matrix $\frac1p XX^T$, where $X$ is a $n\times
p$ matrix with independent entries and the distribution function of the
Marchenko-Pastur law is of order $O(n^{-1/2})$. The bounds hold {\it uniformly}
for any $p$, including $\frac pn$ equal or close to 1.

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