Bernoulli

Rate of convergence in probability to the Marchenko-Pastur law

Friedrich Götze and Alexander Tikhomirov

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Abstract

It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance matrix (1/p)XXT, where X is an n×p matrix with independent entries and the distribution function of the Marchenko-Pastur law is of order O(n-1/2) in probability. The bound is explicit and requires that the twelfth moment of the entries of the matrix is uniformly bounded and that p/n is separated from 1.

Article information

Source
Bernoulli Volume 10, Number 3 (2004), 503-548.

Dates
First available: 7 July 2004

Permanent link to this document
http://projecteuclid.org/euclid.bj/1089206408

Mathematical Reviews number (MathSciNet)
MR2061442

Zentralblatt MATH identifier
1049.60018

Digital Object Identifier
doi:10.3150/bj/1089206408

Citation

Götze, Friedrich; Tikhomirov, Alexander. Rate of convergence in probability to the Marchenko-Pastur law. Bernoulli 10 (2004), no. 3, 503--548. doi:10.3150/bj/1089206408. http://projecteuclid.org/euclid.bj/1089206408.


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References

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