Asymptotic distribution of quadratic forms

Götze F, Tikhomirov AN (1999)
ANNALS OF PROBABILITY 27(2): 1072-1098.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Götze, FriedrichUniBi; Tikhomirov, AN
Abstract / Bemerkung
We consider quadratic forms [GRAPHICS] where X-j are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q(n), and the distribution of the same quadratic forms with X-j replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well. as to nonstationary AR(1) processes.
Stichworte
limit theorems; asymptotic distribution; quadratic forms; independent random variables; Berry-Esseen bounds
Erscheinungsjahr
1999
Zeitschriftentitel
ANNALS OF PROBABILITY
Band
27
Ausgabe
2
Seite(n)
1072-1098
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/1622394

Zitieren

Götze F, Tikhomirov AN. Asymptotic distribution of quadratic forms. ANNALS OF PROBABILITY. 1999;27(2):1072-1098.
Götze, F., & Tikhomirov, A. N. (1999). Asymptotic distribution of quadratic forms. ANNALS OF PROBABILITY, 27(2), 1072-1098.
Götze, F., and Tikhomirov, A. N. (1999). Asymptotic distribution of quadratic forms. ANNALS OF PROBABILITY 27, 1072-1098.
Götze, F., & Tikhomirov, A.N., 1999. Asymptotic distribution of quadratic forms. ANNALS OF PROBABILITY, 27(2), p 1072-1098.
F. Götze and A.N. Tikhomirov, “Asymptotic distribution of quadratic forms”, ANNALS OF PROBABILITY, vol. 27, 1999, pp. 1072-1098.
Götze, F., Tikhomirov, A.N.: Asymptotic distribution of quadratic forms. ANNALS OF PROBABILITY. 27, 1072-1098 (1999).
Götze, Friedrich, and Tikhomirov, AN. “Asymptotic distribution of quadratic forms”. ANNALS OF PROBABILITY 27.2 (1999): 1072-1098.