IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws131211.html
   My bibliography  Save this paper

Bayesian multivariate Bernstein polynomial density estimation

Author

Listed:
  • Wiper, Michael Peter
  • Zhao, Yanyun
  • Ausín Olivera, María Concepción

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

Suggested Citation

  • Wiper, Michael Peter & Zhao, Yanyun & Ausín Olivera, María Concepción, 2013. "Bayesian multivariate Bernstein polynomial density estimation," DES - Working Papers. Statistics and Econometrics. WS ws131211, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws131211
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/16965/WS131211.pdf?sequence=1
    Download Restriction: no

    References listed on IDEAS

    as
    1. 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.
    2. Axel Tenbusch, 1994. "Two-dimensional Bernstein polynomial density estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 233-253, December.
    3. Jara, Alejandro & Hanson, Timothy & Quintana, Fernando A. & Müller, Peter & Rosner, Gary L., 2011. "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i05).
    4. 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(3), pages 535-562, June.
    5. 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, September.
    6. Lorenzo Trippa & Paolo Bulla & Sonia Petrone, 2011. "Extended Bernstein prior via reinforced urn processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 481-496, June.
    7. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    8. 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, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.
    2. Andrés F. Barrientos & Alejandro Jara & Fernando A. Quintana, 2017. "Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 806-825, April.
    3. Gard, Charlotte C. & Brown, Elizabeth R., 2015. "A Bayesian hierarchical model for estimating and partitioning Bernstein polynomial density functions," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 73-83.
    4. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    5. Alexandre Leblanc, 2010. "A bias-reduced approach to density estimation using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 459-475.
    6. Bouezmarni Taoufik & Ghouch El & Taamouti Abderrahim, 2013. "Bernstein estimator for unbounded copula densities," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 343-360, December.
    7. Kim, Dong-Hyuk, 2013. "Optimal choice of a reserve price under uncertainty," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 587-602.
    8. Lu, Lu, 2015. "On the uniform consistency of the Bernstein density estimator," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 52-61.
    9. Bouezmarni, Taoufik & El Ghouch, Anouar & Taamouti, Abderrahim, 2011. "Bernstein Estimator for Unbounded Density Copula," LIDAM Discussion Papers ISBA 2011027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Yuhui Chen & Timothy Hanson & Jiajia Zhang, 2014. "Accelerated hazards model based on parametric families generalized with Bernstein polynomials," Biometrics, The International Biometric Society, vol. 70(1), pages 192-201, March.
    11. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    12. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    13. Stefano Tonellato, 2019. "Bayesian nonparametric clustering as a community detection problem," Working Papers 2019: 20, Department of Economics, University of Venice "Ca' Foscari".
    14. Taamouti, Abderrahim & El Ghouch, Anouar & Bouezmarni, Taoufik, 2011. "Bernstein estimator for unbounded density copula," UC3M Working papers. Economics we1143, Universidad Carlos III de Madrid. Departamento de Economía.
    15. Wiper, Michael Peter & Carnicero, José Antonio & Ausín Olivera, María Concepción, 2010. "Circular Bernstein polynomial distributions," DES - Working Papers. Statistics and Econometrics. WS ws102511, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Tonellato, Stefano F., 2020. "Bayesian nonparametric clustering as a community detection problem," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    17. Jim E. Griffin & Fabrizio Leisen, 2017. "Compound random measures and their use in Bayesian non-parametrics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 525-545, March.
    18. Lorenzo Trippa & Paolo Bulla & Sonia Petrone, 2011. "Extended Bernstein prior via reinforced urn processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 481-496, June.
    19. Sonia Petrone & Piero Veronese, 2002. "Non parametric mixture priors based on an exponential random scheme," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(1), pages 1-20, February.
    20. Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2016. "Bernstein estimation for a copula derivative with application to conditional distribution and regression functionals," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 351-374, June.

    More about this item

    Keywords

    Bayesian nonparametrics;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:ws131211. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ana Poveda). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.