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On the central limit theorem in R p when p→∞
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  • Published: November 1986

On the central limit theorem in R p when p→∞

  • Stephen Portnoy1 

Probability Theory and Related Fields volume 73, pages 571–583 (1986)Cite this article

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Summary

Let X 1 , X 2 , ..., X n be i.i.d. random vectors in R p where p tends to infinity. A theorem is presented showing that the Central Limit Theorem should hold if p 2/n tends to zero. Furthermore, an example is presented with X i having a mixed multivariate normal distribution (with finite moment generating function) for which a uniform normal approximation to the distribution of the sample mean \((\sqrt {\text{n}} \overline {\text{X}} )\) can not hold if p 2/n does not tend to zero.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Altgeld Hall, 61801, Urbana, IL, USA

    Stephen Portnoy

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  1. Stephen Portnoy
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Additional information

Research supported in part by National Science Foundation Grants MCS 80-02340, MCS 83-01834, and DMS 85-03785

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Portnoy, S. On the central limit theorem in R p when p→∞. Probab. Th. Rel. Fields 73, 571–583 (1986). https://doi.org/10.1007/BF00324853

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  • Received: 26 February 1984

  • Issue Date: November 1986

  • DOI: https://doi.org/10.1007/BF00324853

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Keywords

  • Normal Distribution
  • Generate Function
  • Stochastic Process
  • Probability Theory
  • Limit Theorem
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