On the estimation of entropy

Peter Hall, Sally C. Morton

Research output: Contribution to journalArticlepeer-review

129 Scopus citations


Motivated by recent work of Joe (1989, Ann. Inst. Statist. Math., 41, 683-697), we introduce estimators of entropy and describe their properties. We study the effects of tail behaviour, distribution smoothness and dimensionality on convergence properties. In particular, we argue that root-n consistency of entropy estimation requires appropriate assumptions about each of these three features. Our estimators are different from Joe's, and may be computed without numerical integration, but it can be shown that the same interaction of tail behaviour, smoothness and dimensionality also determines the convergence rate of Joe's estimator. We study both histogram and kernel estimators of entropy, and in each case suggest empirical methods for choosing the smoothing parameter.

Original languageEnglish (US)
Pages (from-to)69-88
Number of pages20
JournalAnnals of the Institute of Statistical Mathematics
Issue number1
StatePublished - Mar 1993
Externally publishedYes


  • Convergence rates
  • density estimation
  • entropy
  • histogram estimator
  • kernel estimator
  • projection pursuit
  • root-n consistency

ASJC Scopus subject areas

  • Statistics and Probability


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