Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

Abstract

A method for finding asymptotic lower bounds on information divergence is developed and used to determine the rate of convergence in the Central Limit Theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amari, S.I.: Information geometry on hierarchy of probability distributions. IEEE Trans. Inform. Theory 47, 1701–1711 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cover, T., Thomas, J.A.: Elements of Information Theory. Wiley, Chichester (1991)

    Book  MATH  Google Scholar 

  3. Feller, W.: An Introduction to Probability Theory and its Applications, 2nd edn., vol. 2. Wiley, New York (1971)

    MATH  Google Scholar 

  4. Gupta, A.K., Móri, T.F., Székely, G.J.: Testing for Poissonity-normality vs. other infinite divisibility. Stat. Prabab. Letters 19, 245–248 (1994)

    Article  MATH  Google Scholar 

  5. Harremoës, P.: Convergence to the Poisson distribution in information divergence, Technical Report 2, Mathematical department, University of Copenhagen (2003)

    Google Scholar 

  6. Jaynes, E.T.: Information theory and statistical mechanics, I and II. Physical Reviews 106 and 108, 620–630, 171–190 (1957)

    Google Scholar 

  7. Johnson, O., Barron, A.: Fisher information inequalities and the central limit theorem (preprint, 2001)

    Google Scholar 

  8. Klaassen, C.A.J., Mokveld, P.J., van Es, B.: Squared skewness minus kurtosis bounded by 186/125 for unimodal distributions. Statistical and Probability Letters 50(2), 131–135 (2000)

    Article  MATH  Google Scholar 

  9. Kondratenko, A.E.: The relation between a rate of convergence of moments of normed sums and the Chebyshev-Hermite moments. Theory Probab. Appl. 46(2), 352–355 (2002)

    Article  MathSciNet  Google Scholar 

  10. Mayer-Wolf, E.: The Cramér-Rao functional and limiting laws. Ann. of Probab. 18, 840–850 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Pearson, K.: Mathematical contributions to the theory of evolution, xix; second supplement to a memoir on skew variation. Philos. Trans. Roy. Soc. London Ser. A 216, 257–429 (1916)

    Google Scholar 

  12. Rohatgi, V.K., Székely, G.J.: Sharp inequalities between skewness and kurtosis. Statist. Probab. Lett. 8, 197–299 (1989)

    Article  MathSciNet  Google Scholar 

  13. Topsøe, F.: Information theoretical optimization techniques. Kybernetika 15(1), 8–27 (1979)

    MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Harremoës, P. (2006). Lower Bounds for Divergence in the Central Limit Theorem. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_35

Download citation

  • DOI: https://doi.org/10.1007/11889342_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics