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.