Skip to main content
SpringerLink
Log in

Contrast Functions on Statistical Models

  • Chapter
  • First Online:
Geometric Modeling in Probability and Statistics

  • 3016 Accesses

Abstract

This chapter deals with some important examples of contrastfunctions on a space of density functions, such as: Bregman divergence, Kullback–Leibler relative entropy, f-divergence, Hellinger distance, Chernoff information, Jefferey distance, Kagan divergence, and exponential contrast function. The relation with the skewness tensor and α-connection is made. The goal of this chapter is to produce hands-on examples for the theoretical concepts introduced in Chap. 11.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 89.99
Price excludes VAT (USA)
  • Durable hardcover 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

Bibliography

  1. H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on a sum of observations. Ann. Math. Stat. 23, 493–507 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  2. I. Csiszár, Information type measures of difference of probability distributions and indirect observations. Stud. Sci. Math. Hung. 2, 299–318 (1967)

    MATH  Google Scholar 

  3. I. Csiszár, On topological properties of f-divergence. Stud. Sci. Math. Hung. 2, 329–339 (1967)

    MATH  Google Scholar 

  4. S. Eguchi, A differential geometric approach to statistical inference on the bias of contrast functionals. Hiroshima Math. J. 15, 341–391 (1985)

    MATH  MathSciNet  Google Scholar 

  5. H. Jeffreys, Theory of Probability Theory, 2nd edn. (Oxford University Press, Oxford, 1948)

    MATH  Google Scholar 

  6. A.M. Kagan, On the theory of Fisher’s amount of information. Dokl. Akad. Nauk SSSR 151, 277–278 (1963)

    MathSciNet  Google Scholar 

  7. R.E. Kass, P.W. Vos, Geometrical Foundations of Asymptotic Inference, Wiley Series in Probability and Statistics (Wiley, New York, 1997)

    Book  Google Scholar 

  8. S. Kullback, R.A. Leibler, On information and sufficiency. Ann. Math. Stat. 22, 79 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  9. S. Kullback, R.A. Leibler, Letter to the editor: The KullbackLeibler distance. Am. Stat. 41(4), 340341 (1987). JSTOR 2684769

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Eastern Michigan University, Ypsilanti, MI, USA

    Ovidiu Calin

  2. Faculty of Applied Sciences Department of Mathematics-Informatics, University Politehnica of Bucharest, Bucharest, Romania

    Constantin Udrişte

Authors
  1. Ovidiu Calin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Constantin Udrişte
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Calin, O., Udrişte, C. (2014). Contrast Functions on Statistical Models. In: Geometric Modeling in Probability and Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-07779-6_12

Download citation

Publish with us

Policies and ethics

Search

Navigation