Constructing irregular histograms by penalized likelihood - Yves Rozenholc; Thoralf Mildenberger; Ursula Gather (Technische Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2009)
We propose a fully automatic procedure for the construction of irregular histograms. For a given number of bins, the maximum likelihood histogram is known to be the result of a dynamic programming algorithm. To choose the number of bins, we propose two different penalties motivated by recent work in model selection by Castellan [6] and Massart [26]. We give a complete description of the algorithm and a proper tuning of the penalties. Finally, we compare our procedure to other existing proposals for a wide range of different densities and sample sizes.
Keywords: 519; irregular histogram; density estimation; penalized likelihood; dynamic programming