IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v112y2017i518p806-825.html
   My bibliography  Save this article

Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials

Author

Listed:
  • Andrés F. Barrientos
  • Alejandro Jara
  • Fernando A. Quintana

Abstract

We propose a novel class of probability models for sets of predictor-dependent probability distributions with bounded domain. The proposal extends the Dirichlet–Bernstein prior for single density estimation, by using dependent stick-breaking processes. A general model class and two simplified versions are discussed in detail. Appealing theoretical properties such as continuity, association structure, marginal distribution, large support, and consistency of the posterior distribution are established for all models. The behavior of the models is illustrated using simulated and real-life data. The simulated data are also used to compare the proposed methodology to existing methods. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:806-825
    DOI: 10.1080/01621459.2016.1180987
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2016.1180987
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2016.1180987?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    3. A. Jara & T. E. Hanson, 2011. "A class of mixtures of dependent tail-free processes," Biometrika, Biometrika Trust, vol. 98(3), pages 553-566.
    4. 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.
    5. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
    6. Lorenzo Trippa & Peter Müller & Wesley Johnson, 2011. "The multivariate beta process and an extension of the Polya tree model," Biometrika, Biometrika Trust, vol. 98(1), pages 17-34.
    7. 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.
    8. Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
    9. 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).
    10. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
    11. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    12. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    13. A. Bhattacharya & D. B. Dunson, 2011. "Sparse Bayesian infinite factor models," Biometrika, Biometrika Trust, vol. 98(2), pages 291-306.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    3. Li, Yunzhe & Lee, Juhee & Kottas, Athanasios, 2024. "Bayesian nonparametric Erlang mixture modeling for survival analysis," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    4. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    5. Brian Hart & Michele Guindani & Stephen Malone & Mark Fiecas, 2022. "A nonparametric Bayesian model for estimating spectral densities of resting‐state EEG twin data," Biometrics, The International Biometric Society, vol. 78(1), pages 313-323, March.

    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. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    2. Antonio Lijoi & Bernardo Nipoti, 2013. "A class of hazard rate mixtures for combining survival data from different experiments," DEM Working Papers Series 059, University of Pavia, Department of Economics and Management.
    3. Antonio Lijoi & Bernardo Nipoti, 2014. "A Class of Hazard Rate Mixtures for Combining Survival Data From Different Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 802-814, June.
    4. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    5. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
    6. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    7. repec:cte:wsrepe:ws131211 is not listed on IDEAS
    8. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    9. Chen, Kunzhi & Shen, Weining & Zhu, Weixuan, 2023. "Covariate dependent Beta-GOS process," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    10. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    11. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 1-31, February.
    12. repec:jss:jstsof:40:i05 is not listed on IDEAS
    13. Huang, Yifan & Meng, Shengwang, 2020. "A Bayesian nonparametric model and its application in insurance loss prediction," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 84-94.
    14. 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.
    15. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
    16. Richardson, Robert & Hartman, Brian, 2018. "Bayesian nonparametric regression models for modeling and predicting healthcare claims," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 1-8.
    17. 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.
    18. González, Jorge & Barrientos, Andrés F. & Quintana, Fernando A., 2015. "Bayesian nonparametric estimation of test equating functions with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 222-244.
    19. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    21. Leisen, Fabrizio, 2013. "A multivariate extension of a vector of Poisson- Dirichlet processes," DES - Working Papers. Statistics and Econometrics. WS ws132220, Universidad Carlos III de Madrid. Departamento de Estadística.
    22. Li, Yunzhe & Lee, Juhee & Kottas, Athanasios, 2024. "Bayesian nonparametric Erlang mixture modeling for survival analysis," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

    More about this item

    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:taf:jnlasa:v:112:y:2017:i:518:p:806-825. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.