A comparison of automatic histogram constructions

Davies, Laurie; Gather, Ursula; Nordman, Dan; Weinert, Henrike

doi:10.1051/ps:2008005

Davies, Laurie ; Gather, Ursula ; Nordman, Dan ; Weinert, Henrike

ESAIM: Probability and Statistics, Tome 13 (2009), pp. 181-196.

Résumé

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.

DOI : 10.1051/ps:2008005

Classification : 62G05, 62G07
Mots-clés : regular histogram, model selection, penalized likelihood, taut string

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     author = {Davies, Laurie and Gather, Ursula and Nordman, Dan and Weinert, Henrike},
     title = {A comparison of automatic histogram constructions},
     journal = {ESAIM: Probability and Statistics},
     pages = {181--196},
     publisher = {EDP-Sciences},
     volume = {13},
     year = {2009},
     doi = {10.1051/ps:2008005},
     mrnumber = {2518545},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2008005/}
}

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Davies, Laurie; Gather, Ursula; Nordman, Dan; Weinert, Henrike. A comparison of automatic histogram constructions. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 181-196. doi : 10.1051/ps:2008005. http://www.numdam.org/articles/10.1051/ps:2008005/

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