Issue ESAIM: PS Volume 13, 2009 Page(s) 181 - 196 DOI 10.1051/ps:2008005 Published online 11 June 2009

ESAIM: PS, June 2009, Vol. 13, p. 181-196
DOI: 10.1051/ps:2008005

A comparison of automatic histogram constructions

Laurie Davies¹, Ursula Gather², Dan Nordman³ and Henrike Weinert<sup>4

1</sup>  Department of Mathematics, University Duisburg-Essen; Department of Mathematics, Technical University Eindhoven, Germany.
²  Department of Statistics, Technische Universität Dortmund, Germany; gather@statistik.uni.dortmund.de
³  Department of Statistics, Iowa State University, USA.
⁴  Department of Statistics, Technische Universität Dortmund, Germany.

Received April 26, 2007. Revised February 13, 2008. Published online 11 June 2009

Abstract
Even for a well-trained statistician the construction of a histogram for a given real-valued data set is a difficult problem. It is even more difficult to construct a fully automatic procedure which specifies the number and widths of the bins in a satisfactory manner for a wide range of data sets. In this paper we compare several histogram construction procedures by means of a simulation study. 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.

Mathematics Subject Classification. 62G05, 62G07

Key words: Regular histogram, model selection, penalized likelihood, taut string


© EDP Sciences, SMAI 2009

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