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Convergence determining sets in the central limit theorem
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  • Published: January 1986

Convergence determining sets in the central limit theorem

  • Peter Hall1 &
  • J. C. H. Wightwick1 

Probability Theory and Related Fields volume 71, pages 1–17 (1986)Cite this article

  • 93 Accesses

  • 2 Citations

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Summary

A complete characterisation is given of the class of all doublets which determine the rate of convergence in the central limit theorem. This enables a number of important properties of convergence determining sets to be deduced. In particular, it is shown that no singleton can be convergence determining, and any set consisting of four or more distinct points is convergence determining. Numerical and analytic methods are used to derive the geometry of the class of all convergence determining doublets.

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References

  1. Hall, P.: Rates of convergence in the central limit theorem. London: Pitman 1982

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  2. Hall, P.: Sets which determine the rate of convergence in the central limit theorem. Ann. Probab. 11, 355–361 (1983)

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  3. Heyde, C.C., Nakata, T.: On the asymptotic equivalence of L p metrics for convergence to normality. To appear

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Author information

Authors and Affiliations

  1. Dept. of Statistics, Australian National University, GPO Box 4, 2601, Canberra, ACT, Australia

    Peter Hall & J. C. H. Wightwick

Authors
  1. Peter Hall
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  2. J. C. H. Wightwick
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Cite this article

Hall, P., Wightwick, J.C.H. Convergence determining sets in the central limit theorem. Probab. Th. Rel. Fields 71, 1–17 (1986). https://doi.org/10.1007/BF00366269

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  • Received: 25 May 1984

  • Issue Date: January 1986

  • DOI: https://doi.org/10.1007/BF00366269

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Keywords

  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Mathematical Biology
  • Central Limit
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