Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space

Bogatyrev SA, Götze F, Ulyanov VV (2006)
JOURNAL OF MULTIVARIATE ANALYSIS 97(9): 2041-2056.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
We consider short asymptotic expansions for the probability of a sum of i.i.d. random elements to hit a ball in a Hilbert space H. The error bound for the expansion is of order O(n(-1)). It depends on the first 12 eigenvalues of the covariance operator only. Moreover, the bound is non-uniform, i.e. the accuracy of the approximation becomes better as the distance between a boundary of the ball and the origin in H grows. (c) 2006 Elsevier Inc. All rights reserved.
Stichworte
central limit theorem; Gaussian approximation; Edgeworth; expansions; Hilbert space; covariance operator
Erscheinungsjahr
2006
Zeitschriftentitel
JOURNAL OF MULTIVARIATE ANALYSIS
Band
97
Ausgabe
9
Seite(n)
2041-2056
ISSN
0047-259X
Page URI
https://pub.uni-bielefeld.de/record/1597582

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Bogatyrev SA, Götze F, Ulyanov VV. Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space. JOURNAL OF MULTIVARIATE ANALYSIS. 2006;97(9):2041-2056.
Bogatyrev, S. A., Götze, F., & Ulyanov, V. V. (2006). Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space. JOURNAL OF MULTIVARIATE ANALYSIS, 97(9), 2041-2056. doi:10.1016/j.jmva.2006.01.010
Bogatyrev, S. A., Götze, F., and Ulyanov, V. V. (2006). Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space. JOURNAL OF MULTIVARIATE ANALYSIS 97, 2041-2056.
Bogatyrev, S.A., Götze, F., & Ulyanov, V.V., 2006. Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space. JOURNAL OF MULTIVARIATE ANALYSIS, 97(9), p 2041-2056.
S.A. Bogatyrev, F. Götze, and V.V. Ulyanov, “Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space”, JOURNAL OF MULTIVARIATE ANALYSIS, vol. 97, 2006, pp. 2041-2056.
Bogatyrev, S.A., Götze, F., Ulyanov, V.V.: Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space. JOURNAL OF MULTIVARIATE ANALYSIS. 97, 2041-2056 (2006).
Bogatyrev, S. A., Götze, Friedrich, and Ulyanov, V. V. “Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space”. JOURNAL OF MULTIVARIATE ANALYSIS 97.9 (2006): 2041-2056.