A comparison of automatic histogram constructions

Laurie Davies (1, 2) , Ursula Gather (3) , Dan Nordman (4) , Henrike Weinert (3)

1 Department of Mathematics
2 Department of mathematics and computing science [Eindhoven]
3 Department of Statistics
4 Department of Statistics

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.

Mots clés: Mathematics

Laurie Davies, Ursula Gather, Dan Nordman, Henrike Weinert. A comparison of automatic histogram constructions. ESAIM: Probability and Statistics, 2009, 13, pp.181-196. ⟨10.1051/ps:2008005⟩. ⟨hal-00491251⟩