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The Generalized Cross Entropy Method, with Applications to Probability Density Estimation

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  • Zdravko I. Botev

    (The University of Queensland)

  • Dirk P. Kroese

    (The University of Queensland)

Abstract

Nonparametric density estimation aims to determine the sparsest model that explains a given set of empirical data and which uses as few assumptions as possible. Many of the currently existing methods do not provide a sparse solution to the problem and rely on asymptotic approximations. In this paper we describe a framework for density estimation which uses information-theoretic measures of model complexity with the aim of constructing a sparse density estimator that does not rely on large sample approximations. The effectiveness of the approach is demonstrated through an application to some well-known density estimation test cases.

Suggested Citation

  • Zdravko I. Botev & Dirk P. Kroese, 2011. "The Generalized Cross Entropy Method, with Applications to Probability Density Estimation," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 1-27, March.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:1:d:10.1007_s11009-009-9133-7
    DOI: 10.1007/s11009-009-9133-7
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    References listed on IDEAS

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    1. Hall, Peter & Turlach, Berwin A., 1999. "Reducing bias in curve estimation by use of weights," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 67-86, March.
    2. Zdravko I. Botev & Dirk P. Kroese, 2008. "Non-asymptotic Bandwidth Selection for Density Estimation of Discrete Data," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 435-451, September.
    3. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    4. A. Ben-Tal & M. Teboulle, 1987. "Penalty Functions and Duality in Stochastic Programming Via (phi)-Divergence Functionals," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 224-240, May.
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    6. K. E. Basford & G. J. Mclachlan & M. G. York, 1997. "Modelling the distribution of stamp paper thickness via finite normal mixtures: The 1872 Hidalgo stamp issue of Mexico revisited," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(2), pages 169-180.
    7. R. Y. Rubinstein, 2005. "A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 5-50, March.
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    Cited by:

    1. Joshua C. C. Chan & Eric Eisenstat, 2015. "Marginal Likelihood Estimation with the Cross-Entropy Method," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 256-285, March.
    2. Deyan Radev, 2012. "Systemic Risk, Banking and Sovereign Debt in the Euro Area," Working Papers 1207, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    3. Radev, Deyan, 2013. "Systemic risk and sovereign debt in the Euro area," SAFE Working Paper Series 37, Leibniz Institute for Financial Research SAFE.
    4. F. J. Alonso & M. C. Bueso & J. M. Angulo, 2016. "Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 921-933, September.
    5. Guarino, Francesco & Cassarà, Pietro & Longo, Sonia & Cellura, Maurizio & Ferro, Erina, 2015. "Load match optimisation of a residential building case study: A cross-entropy based electricity storage sizing algorithm," Applied Energy, Elsevier, vol. 154(C), pages 380-391.

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