Journal of Statistical Theory and Practice

, Volume 2, Issue 2, pp 221–232 | Cite as

A Cautionary Note on Model Choice and the Kullback-Leibler Information

  • C. C. HeydeEmail author
  • K. All


The Kullback-Leibler information has found application in many areas of statistical science. It typically arises in model choice and model dimension questions in a way which suggests its use as a distance. Indeed, it has been widely described as a distance although it comprehensively fails to be a metric. Some pitfalls in interpreting it as a distance are discussed and, in particular, its application to discriminate between prospective risky asset returns distributions.


Discrimination Entropy Heavy-tailed Statistical distance 

AMS Subject Classification

62G32 62P05 94A17 


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Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Mathematical Sciences InstituteAustralian National UniversityACTAustralia
  3. 3.Department of Mathematics and StatisticsUniversity of MelbourneAustralia

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