IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v103y2016icp229-241.html
   My bibliography  Save this article

Functional regression approximate Bayesian computation for Gaussian process density estimation

Author

Listed:
  • Rodrigues, G.S.
  • Nott, David J.
  • Sisson, S.A.

Abstract

A novel Bayesian nonparametric method is proposed for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a major challenge in this context. To address this problem, a hierarchically structured prior, defined over a set of univariate density functions using convenient transformations of Gaussian processes, is introduced. Inference is performed through approximate Bayesian computation (ABC) via a novel functional regression adjustment. The performance of the proposed method is illustrated via simulation studies and an analysis of rural high school exam performance in Brazil.

Suggested Citation

  • Rodrigues, G.S. & Nott, David J. & Sisson, S.A., 2016. "Functional regression approximate Bayesian computation for Gaussian process density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 229-241.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:229-241
    DOI: 10.1016/j.csda.2016.05.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947316301116
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2016.05.009?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. Gery Geenens & Arthur Charpentier & Davy Paindaveine, 2014. "Probit Transformation for Nonparametric Kernel Estimation of the Copula Density," Working Papers ECARES ECARES 2014-23, ULB -- Universite Libre de Bruxelles.
    3. Dai, J. & Sperlich, S., 2010. "Simple and effective boundary correction for kernel densities and regression with an application to the world income and Engel curve estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2487-2497, November.
    4. Gery Geenens, 2014. "Probit Transformation for Kernel Density Estimation on the Unit Interval," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 346-358, March.
    5. Peter Müller & Fernando Quintana & Gary Rosner, 2004. "A method for combining inference across related nonparametric Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 735-749, August.
    6. Blum, Michael G. B., 2010. "Approximate Bayesian Computation: A Nonparametric Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1178-1187.
    7. M.C. Jones & D.A. Henderson, 2007. "Miscellanea Kernel-Type Density Estimation on the Unit Interval," Biometrika, Biometrika Trust, vol. 94(4), pages 977-984.
    8. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    9. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    10. 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).
    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. Boris Beranger & Huan Lin & Scott Sisson, 2023. "New models for symbolic data analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 659-699, September.

    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. Jesús Fajardo & Pedro Harmath, 2021. "Boundary estimation with the fuzzy set density estimator," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 285-302, December.
    2. Gery Geenens, 2014. "Probit Transformation for Kernel Density Estimation on the Unit Interval," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 346-358, March.
    3. 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.
    4. 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.
    5. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    6. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    7. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes," CIRJE F-Series CIRJE-F-573, CIRJE, Faculty of Economics, University of Tokyo.
    8. Mahsa Samsami & Ralf Wagner, 2021. "Investment Decisions with Endogeneity: A Dirichlet Tree Analysis," JRFM, MDPI, vol. 14(7), pages 1-19, July.
    9. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    10. Igarashi, Gaku & Kakizawa, Yoshihide, 2014. "Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 235-246.
    11. Michael L. Pennell & David B. Dunson, 2008. "Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor," Biometrics, The International Biometric Society, vol. 64(2), pages 413-423, June.
    12. Nagler Thomas & Czado Claudia & Schellhase Christian, 2017. "Nonparametric estimation of simplified vine copula models: comparison of methods," Dependence Modeling, De Gruyter, vol. 5(1), pages 99-120, January.
    13. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    14. Daniela Castro Camilo & Miguel de Carvalho & Jennifer Wadsworth, 2017. "Time-Varying Extreme Value Dependence with Application to Leading European Stock Markets," Papers 1709.01198, arXiv.org.
    15. Bruno Scarpa & David B. Dunson, 2009. "Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors," Biometrics, The International Biometric Society, vol. 65(3), pages 772-780, September.
    16. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    17. George Karabatsos & Stephen Walker, 2009. "A Bayesian Nonparametric Approach to Test Equating," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 211-232, June.
    18. D.P. Amali Dassanayake & Igor Volobouev & A. Alexandre Trindade, 2017. "Local orthogonal polynomial expansion for density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 806-830, October.
    19. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    20. Funke, Benedikt & Hirukawa, Masayuki, 2021. "Bias correction for local linear regression estimation using asymmetric kernels via the skewing method," Econometrics and Statistics, Elsevier, vol. 20(C), pages 109-130.

    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:eee:csdana:v:103:y:2016:i:c:p:229-241. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.