Optimal rates of convergence in the CLT for quadratic forms

Bentkus V, Götze F (1996)
ANNALS OF PROBABILITY 24(1): 466-490.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We prove optimal convergence rates in the central limit theorem for sums in R(k). Assuming a fourth moment, we obtain a Berry-Esseen type bound of O(N-1) for the probability of hitting a ball provided that k greater than or equal to 5. The proof still requires a technical assumption related to the independence of coordinates of sums.
Stichworte
central limit theorem; Berry-Esseen bound; multidimensional spaces; Hilbert space; quadratic forms; ellipsoids; convergence rates
Erscheinungsjahr
1996
Zeitschriftentitel
ANNALS OF PROBABILITY
Band
24
Ausgabe
1
Seite(n)
466-490
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/1638947

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Bentkus V, Götze F. Optimal rates of convergence in the CLT for quadratic forms. ANNALS OF PROBABILITY. 1996;24(1):466-490.
Bentkus, V., & Götze, F. (1996). Optimal rates of convergence in the CLT for quadratic forms. ANNALS OF PROBABILITY, 24(1), 466-490.
Bentkus, V., and Götze, F. (1996). Optimal rates of convergence in the CLT for quadratic forms. ANNALS OF PROBABILITY 24, 466-490.
Bentkus, V., & Götze, F., 1996. Optimal rates of convergence in the CLT for quadratic forms. ANNALS OF PROBABILITY, 24(1), p 466-490.
V. Bentkus and F. Götze, “Optimal rates of convergence in the CLT for quadratic forms”, ANNALS OF PROBABILITY, vol. 24, 1996, pp. 466-490.
Bentkus, V., Götze, F.: Optimal rates of convergence in the CLT for quadratic forms. ANNALS OF PROBABILITY. 24, 466-490 (1996).
Bentkus, V, and Götze, Friedrich. “Optimal rates of convergence in the CLT for quadratic forms”. ANNALS OF PROBABILITY 24.1 (1996): 466-490.