IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v36y2009i2p337-354.html
   My bibliography  Save this article

Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions

Author

Listed:
  • ROSS McVINISH
  • JUDITH ROUSSEAU
  • KERRIE MENGERSEN

Abstract

. We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non‐parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.

Suggested Citation

  • ROSS McVINISH & JUDITH ROUSSEAU & KERRIE MENGERSEN, 2009. "Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 337-354, June.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:2:p:337-354
    DOI: 10.1111/j.1467-9469.2008.00620.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2008.00620.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2008.00620.x?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
    ---><---

    References listed on IDEAS

    as
    1. F. Perron & K. Mengersen, 2001. "Bayesian Nonparametric Modeling Using Mixtures of Triangular Distributions," Biometrics, The International Biometric Society, vol. 57(2), pages 518-528, June.
    2. Miguel Arcones, 2002. "Moderate deviations for M-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 465-500, December.
    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, January.
    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. Gwangsu Kim & Yongdai Kim & Taeryon Choi, 2017. "Bayesian Analysis of the Proportional Hazards Model with Time-Varying Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 524-544, June.
    2. Angela Schörgendorfer & Adam J. Branscum & Timothy E. Hanson, 2013. "A Bayesian Goodness of Fit Test and Semiparametric Generalization of Logistic Regression with Measurement Data," Biometrics, The International Biometric Society, vol. 69(2), pages 508-519, June.
    3. Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.
    4. Surya T. Tokdar & Ryan Martin, 2021. "Bayesian Test of Normality Versus a Dirichlet Process Mixture Alternative," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 66-96, May.
    5. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    6. Vaidehi Dixit & Ryan Martin, 2022. "Estimating a Mixing Distribution on the Sphere Using Predictive Recursion," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 596-626, November.
    7. repec:dau:papers:123456789/13438 is not listed 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. repec:jss:jstsof:40:i05 is not listed on IDEAS
    2. Yao Luo & Peijun Sang & Ruli Xiao, 2024. "Order Statistics Approaches to Unobserved Heterogeneity in Auctions," Working Papers tecipa-776, University of Toronto, Department of Economics.
    3. repec:cte:wsrepe:ws131211 is not listed on IDEAS
    4. Guillin, A. & Liptser, R., 2005. "MDP for integral functionals of fast and slow processes with averaging," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1187-1207, July.
    5. 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.
    6. 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.
    7. Han, Bing & Dalal, Siddhartha R., 2012. "A Bernstein-type estimator for decreasing density with application to p-value adjustments," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 427-437.
    8. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    9. Carnicero, José Antonio, 2008. "A semi-parametric model for circular data based on mixtures of beta distributions," DES - Working Papers. Statistics and Econometrics. WS ws081305, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Fisher, Mark & Jensen, Mark J., 2019. "Bayesian inference and prediction of a multiple-change-point panel model with nonparametric priors," Journal of Econometrics, Elsevier, vol. 210(1), pages 187-202.
    11. Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, January.
    12. McVinish, R. & Mengersen, K., 2008. "Semiparametric Bayesian circular statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4722-4730, June.
    13. Mark F. J. Steel & Francisco J. Rubio, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(2), pages 218-222, August.
    14. Jiajia Zhang & Timothy Hanson & Haiming Zhou, 2019. "Bayes factors for choosing among six common survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 361-379, April.
    15. Carnicero, José Antonio, 2010. "Circular Bernstein polynomial distributions," DES - Working Papers. Statistics and Econometrics. WS ws102511, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Ghosh, Sujit K. & Burns, Christopher B. & Prager, Daniel L. & Zhang, Li & Hui, Glenn, 2018. "On nonparametric estimation of the latent distribution for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 86-98.
    17. 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.
    18. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    19. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    20. 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.
    21. Lopes, Hedibert F. & Dias, Ronaldo, 2011. "Bayesian mixture of parametric and nonparametric density estimation: A Misspecification Problem," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 31(1), March.
    22. Patricio Maturana-Russel & Renate Meyer, 2021. "Bayesian spectral density estimation using P-splines with quantile-based knot placement," Computational Statistics, Springer, vol. 36(3), pages 2055-2077, September.

    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:bla:scjsta:v:36:y:2009:i:2:p:337-354. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.