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Fisher information inequalities and the central limit theorem
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  • Published: 29 April 2004

Fisher information inequalities and the central limit theorem

  • Oliver Johnson1 &
  • Andrew Barron2 

Probability Theory and Related Fields volume 129, pages 391–409 (2004)Cite this article

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Abstract.

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L 2 spaces and Poincaré inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it converges to zero.

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Author information

Authors and Affiliations

  1. Statslab, Wilberforce Road, Cambridge, CB3 0WB, UK

    Oliver Johnson

  2. Department of Statistics, Yale University, 208290, New Haven, Connecticut 06520-8290, USA

    Andrew Barron

Authors
  1. Oliver Johnson
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  2. Andrew Barron
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Corresponding author

Correspondence to Oliver Johnson.

Additional information

OTJ is a Fellow of Christ’s College, Cambridge, who helped support two trips to Yale University during which this paper was written.

Mathematics Subject Classification (2000):Primary: 62B10 Secondary: 60F05, 94A17

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Johnson, O., Barron, A. Fisher information inequalities and the central limit theorem. Probab. Theory Relat. Fields 129, 391–409 (2004). https://doi.org/10.1007/s00440-004-0344-0

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  • Received: 07 July 2003

  • Revised: 22 January 2004

  • Published: 29 April 2004

  • Issue Date: July 2004

  • DOI: https://doi.org/10.1007/s00440-004-0344-0

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Key words or phrases:

  • Normal convergence
  • Entropy
  • Fisher information
  • Poincaré
  • inequalities
  • Rates of convergence
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