This article is cited in 11 papers

The Rate of Convergence of Spectra of Sample Covariance Matrices

F. Götze, A. N. Tikhomirov

Bielefeld University

Abstract: 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, Marchenko–Pastur distribution, spectral distribution function.

Received: 25.08.2008

Language: English

DOI: 10.4213/tvp2556

 English version: Theory of Probability and its Applications, 2010, 54:1, 129–140

Bibliographic databases:

• 
• 
•