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Combining regular and irregular histograms by penalized likelihood

Author

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  • Rozenholc, Yves
  • Mildenberger, Thoralf
  • Gather, Ursula

Abstract

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

Suggested Citation

  • Rozenholc, Yves & Mildenberger, Thoralf & Gather, Ursula, 2010. "Combining regular and irregular histograms by penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3313-3323, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3313-3323
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    References listed on IDEAS

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    1. F. Comte & Y. Rozenholc, 2004. "A new algorithm for fixed design regression and denoising," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 449-473, September.
    2. Chen, X. R. & Zhao, L. C., 1987. "Almost sure L1-norm convergence for data-based histogram density estimates," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 179-188, February.
    3. Celisse, Alain & Robin, Stephane, 2008. "Nonparametric density estimation by exact leave-p-out cross-validation," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2350-2368, January.
    4. Luc Devroye & Gábor Lugosi, 2004. "Bin width selection in multivariate histograms by the combinatorial method," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 129-145, June.
    5. Joachim Engel, 1997. "The multiresolution histogram," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 41-57, January.
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    Cited by:

    1. Zelaya Mendizábal, Valentina & Boullé, Marc & Rossi, Fabrice, 2023. "Fast and fully-automated histograms for large-scale data sets," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).

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