Rate of convergence in probability to the Marchenko-Pastur law
Götze, Friedrich ; Tikhomirov, Alexander
Bernoulli, Tome 10 (2004) no. 2, p. 503-548 / Harvested from Project Euclid
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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.
Publié le : 2004-06-14
Classification:  independent random variables,  random matrix,  spectral distribution 
@article{1089206408,
     author = {G\"otze, Friedrich and Tikhomirov, Alexander},
     title = {Rate of convergence in probability to the Marchenko-Pastur law},
     journal = {Bernoulli},
     volume = {10},
     number = {2},
     year = {2004},
     pages = { 503-548},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1089206408}
}

Götze, Friedrich; Tikhomirov, Alexander. Rate of convergence in probability to the Marchenko-Pastur law. Bernoulli, Tome 10 (2004) no. 2, pp.  503-548. http://gdmltest.u-ga.fr/item/1089206408/