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A comparison of automatic histogram constructions

Published online by Cambridge University Press:  11 June 2009

Laurie Davies ,
Ursula Gather ,
Dan Nordman  and
Henrike Weinert
Laurie Davies
Affiliation:
Department of Mathematics, University Duisburg-Essen; Department of Mathematics, Technical University Eindhoven, Germany.
Ursula Gather
Affiliation:
Department of Statistics, Technische Universität Dortmund, Germany; [email protected]
Dan Nordman
Affiliation:
Department of Statistics, Iowa State University, USA.
Henrike Weinert
Affiliation:
Department of Statistics, Technische Universität Dortmund, Germany.
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Abstract

Even for a well-trained statistician the construction of a histogramfor a given real-valued data set is a difficult problem. It is evenmore difficult to construct a fully automatic procedure whichspecifies the number and widths of the bins in a satisfactory mannerfor a wide range of data sets. In this paper we compare severalhistogram construction procedures by means of a simulationstudy. The study includes plug-in methods, cross-validation,penalized maximum likelihood and the taut string procedure. Their performance on different test beds is measured by their ability to identify the peaks of an underlying density as well as by Hellinger distance.

Keywords

Regular histogrammodel selectionpenalized likelihoodtaut string
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 13 , July 2009 , pp. 181 - 196
Copyright
© EDP Sciences, SMAI, 2009

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