Constructing irregular histograms by penalized likelihood
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Date
2009-04-30T10:42:23Z
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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 [1] and Massart [2].
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.
[1] Castellan, G., 1999. Modified Akaike's criterion for histogram density estimation.
Technical Report 99.61, Université de Paris-Sud.
[2] Massart, P., 2007. Concentration inequalities and model selection. Lecture Notes in
Mathematics Vol. 1896, Springer, New York.
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Keywords
density estimation, dynamic programming, irregular histogram, penalized likelihood