Constructing a regular histogram - a comparison of methods

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 methods 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 the Hellinger distance and the ability to identify the modes of the underlying density.