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Bayesian multivariate Bernstein polynomial density estimation

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Author Info

  • Yanyun Zhao

    ()

  • Concepción Ausín

    ()

  • Michael P. Wiper

    ()

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    Abstract

    This paper introduces a new approach to Bayesian nonparametric inference for densities on the hypercube, based on the use of a multivariate Bernstein polynomial prior. Posterior convergence rates under the proposed prior are obtained. Furthermore, a novel sampling scheme, based on the use of slice sampling techniques, is proposed for estimation of the posterior predictive density. The approach is illustrated with both simulated and real data examples

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    File URL: http://e-archivo.uc3m.es/bitstream/10016/16965/1/WS131211.pdf
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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws131211.

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    Date of creation: Jun 2013
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    Handle: RePEc:cte:wsrepe:ws131211

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    Related research

    Keywords: Bayesian nonparametrics; Bernstein polynomials; Dirichlet process;

    This paper has been announced in the following NEP Reports:

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    1. Alejandro Jara & Timothy Hanson & Fernando A. Quintana & Peter Müller & Gary L. Rosner, . "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, American Statistical Association, vol. 40(i05).
    2. Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 26(3), pages 373-393.
    3. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100.
    4. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    5. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    6. Axel Tenbusch, 1994. "Two-dimensional Bernstein polynomial density estimators," Metrika, Springer, vol. 41(1), pages 233-253, December.
    7. Lorenzo Trippa & Paolo Bulla & Sonia Petrone, 2011. "Extended Bernstein prior via reinforced urn processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(3), pages 481-496, June.
    8. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 535-562, June.
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