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Constructing a regular histogram : a comparison of methods

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  • Davies, P. Laurie
  • Gather, Ursula
  • Nordman, Daniel
  • Weinert, Henrike

Abstract

Even for a well-trained statistician the construction of a histogram for a given real-valued set is a sifficult problem. It is even more difficult to construct a fully automatic procedure which specifies the number and widths of the binss in a satisfactory manner for a wide range of data sets. In this paper we compare several histogram construction methods by means of a simulation study. The study includes plug-in methods, cross-validation, penalized maximum likehood and the taut string procedure. Their performance on different test beds is measured by the Hellinger distance and the ability to identify the modes of the underlying density.

Suggested Citation

  • Davies, P. Laurie & Gather, Ursula & Nordman, Daniel & Weinert, Henrike, 2007. "Constructing a regular histogram : a comparison of methods," Technical Reports 2007,14, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200714
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    References listed on IDEAS

    as
    1. Hall, Peter & Wand, Matthew P., 1988. "Minimizing L1 distance in nonparametric density estimation," Journal of Multivariate Analysis, Elsevier, vol. 26(1), pages 59-88, July.
    2. Kanazawa, Yuichiro, 1993. "Hellinger distance and Akaike's information criterion for the histogram," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 293-298, July.
    3. Joachim Engel, 1997. "The multiresolution histogram," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 41-57, January.
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