|Title:||Constructing irregular histograms by penalized likelihood|
|Abstract:||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  and Massart . 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.  Castellan, G., 1999. Modified Akaike's criterion for histogram density estimation. Technical Report 99.61, Université de Paris-Sud.  Massart, P., 2007. Concentration inequalities and model selection. Lecture Notes in Mathematics Vol. 1896, Springer, New York.|
|Subject Headings:||density estimation|
|Appears in Collections:||Sonderforschungsbereich (SFB) 475|
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