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.
