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

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  • Bogatyrev, S.A.
  • Götze, F.
  • Ulyanov, V.V.
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    Abstract

    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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 9 (October)
    Pages: 2041-2056

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:2041-2056

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    Related research

    Keywords: Central limit theorem Hilbert space Gaussian approximation Edgeworth expansions Covariance operator;

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