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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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    3. 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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