Rate of convergence in probability to the Marchenko-Pastur law

Götze F, Tikhomirov A (2004)
BERNOULLI 10(3): 503-548.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance (1/p)XXT, where X is an nxp 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.
Stichworte
independent random variables; spectral distributions; random matrix
Erscheinungsjahr
2004
Zeitschriftentitel
BERNOULLI
Band
10
Ausgabe
3
Seite(n)
503-548
ISSN
1350-7265
Page URI
https://pub.uni-bielefeld.de/record/1606044

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Götze F, Tikhomirov A. Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI. 2004;10(3):503-548.
Götze, F., & Tikhomirov, A. (2004). Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI, 10(3), 503-548.
Götze, F., and Tikhomirov, A. (2004). Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI 10, 503-548.
Götze, F., & Tikhomirov, A., 2004. Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI, 10(3), p 503-548.
F. Götze and A. Tikhomirov, “Rate of convergence in probability to the Marchenko-Pastur law”, BERNOULLI, vol. 10, 2004, pp. 503-548.
Götze, F., Tikhomirov, A.: Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI. 10, 503-548 (2004).
Götze, Friedrich, and Tikhomirov, A. “Rate of convergence in probability to the Marchenko-Pastur law”. BERNOULLI 10.3 (2004): 503-548.