  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.

Probability;Spectral Theory