Combining regular and irregular histograms by penalized likelihood

A new fully automatic procedure for the construction of histograms is proposed. It consists of constructing both a regular and an irregular histogram and then choosing between the two. To choose the number of bins in the irregular histogram, two different penalties motivated by recent work in model selection are proposed. A description of the algorithm and a proper tuning of the penalties is given. Finally, different versions of the procedure are compared to other existing proposals for a wide range of densities and sample sizes. In the simulations, the squared Hellinger risk of the new procedure is always at most twice as large as the risk of the best of the other methods. The procedure is implemented in the R-Package histogram available from CRAN.1