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


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


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.

Suggested Citation

  • 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, Elsevier, vol. 97(9), pages 2041-2056, October.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:2041-2056

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    References listed on IDEAS

    1. Taneichi, Nobuhiro & Sekiya, Yuri & Suzukawa, Akio, 2002. "Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 335-359, May.
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