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

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.

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Year of publication:	2006
Authors:	Bogatyrev, S.A. ; Götze, F. ; Ulyanov, V.V.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 97.2006, 9, p. 2041-2056
Publisher:	Elsevier
Keywords:	Central limit theorem Hilbert space Gaussian approximation Edgeworth expansions Covariance operator

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005221261