Skip to main content
SpringerLink
Log in

A Characterization of Monotone and Regular Divergences

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

In this paper we characterize the local structure of monotone and regular divergences, which include f-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by Čencov, using the invariant properties of Amari's α-connections.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Amari, S. (1985). Differential-geometrical Methods in Statistics, Lecture Notes in Statistics, Vol. 28, Springer, New York.

    Google Scholar 

  • Blæsild, P. (1991). Yokes and tensors derived from yokes, Ann. Inst. Statist. Math., 43(1), 95–113.

    Google Scholar 

  • Burbea, J. (1983). J-divergences and related concepts, Encyclopedia of Statistical Sciences, Vol. 4, 290–296, Wiley, New York.

    Google Scholar 

  • Campbell, L. (1986). An extended Čencov characterization of the information metric, Proc. Amer. Math. Soc., 98, 135–141.

    Google Scholar 

  • Čencov, N. (1972). Statistical Decision Rules and Optimal Inference, Nauka, Moscow (in Russian, English version (1982). Trans. Math. Monographs, 53, American Mathematical Society, Providence).

    Google Scholar 

  • Eguchi, S. (1992). Geometry of minimum contrast, Hiroshima Math. J., 22, 631–647.

    Google Scholar 

  • Heyer, H. (1982). Theory of Statistical Experiments, Springer, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departament d'Estadística, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007, Barcelona, Spain

    J. M. Corcuera

  2. Dipartimento di Scienze Statistiche, Università degli Studi di Padova, Via S. Francesco, 33, 35121, Padova, Italy

    F. Giummolè

Authors
  1. J. M. Corcuera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Giummolè
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Corcuera, J.M., Giummolè, F. A Characterization of Monotone and Regular Divergences. Annals of the Institute of Statistical Mathematics 50, 433–450 (1998). https://doi.org/10.1023/A:1003569210573

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1003569210573

Search

Navigation