- Volume 10, Number 3 (2004), 503-548.
Rate of convergence in probability to the Marchenko-Pastur law
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.
Bernoulli, Volume 10, Number 3 (2004), 503-548.
First available in Project Euclid: 7 July 2004
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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. https://projecteuclid.org/euclid.bj/1089206408