IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i10p2411-2419.html
   My bibliography  Save this article

The L1-consistency of Dirichlet mixtures in multivariate Bayesian density estimation

Author

Listed:
  • Wu, Yuefeng
  • Ghosal, Subhashis

Abstract

Density estimation, especially multivariate density estimation, is a fundamental problem in nonparametric inference. In the Bayesian approach, Dirichlet mixture priors are often used in practice for such problems. However, the asymptotic properties of such priors have only been studied in the univariate case. We extend the L1-consistency of Dirichlet mixutures in the multivariate density estimation setting. We obtain such a result by showing that the Kullback-Leibler property of the prior holds and that the size of the sieve in the parameter space in terms of L1-metric entropy is not larger than the order of n. However, it seems that the usual technique of choosing a sieve by controlling prior probabilities is unable to lead to a useful bound on the metric entropy required for the application of a general posterior consistency theorem for the multivariate case. We overcome this difficulty by using a structural property of Dirichlet mixtures. Our results apply to a multivariate normal kernel even when the multivariate normal kernel has a general variance-covariance matrix.

Suggested Citation

  • Wu, Yuefeng & Ghosal, Subhashis, 2010. "The L1-consistency of Dirichlet mixtures in multivariate Bayesian density estimation," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2411-2419, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2411-2419
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00131-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Woo, Mi-Ja & Sriram, T.N., 2007. "Robust estimation of mixture complexity for count data," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4379-4392, May.
    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. Rabi Bhattacharya & Rachel Oliver, 2019. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-36, February.
    2. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    3. Bhattacharya, Abhishek & Dunson, David, 2012. "Nonparametric Bayes classification and hypothesis testing on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 1-19.
    4. 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.
    5. Julyan Arbel & Riccardo Corradin & Bernardo Nipoti, 2021. "Dirichlet process mixtures under affine transformations of the data," Computational Statistics, Springer, vol. 36(1), pages 577-601, 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. Tang, Qingguo & Karunamuni, Rohana J., 2013. "Minimum distance estimation in a finite mixture regression model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 185-204.
    2. Jamie Cross & Lennart Hoogerheide & Paul Labonne & Herman K. van Dijk, 2023. "Bayesian Mode Inference for Discrete Distributions in Economics and Finance," Tinbergen Institute Discussion Papers 23-038/III, Tinbergen Institute.
    3. Chee, Chew-Seng, 2017. "A mixture model-based nonparametric approach to estimating a count distribution," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 34-44.
    4. Jamie L. Cross & Lennart Hoogerheide & Paul Labonne & Herman K. van Dijk, 2024. "Flexible Negative Binomial Mixtures for Credible Mode Inference in Heterogeneous Count Data from Finance, Economics and Bioinformatics," Tinbergen Institute Discussion Papers 24-056/III, Tinbergen Institute.
    5. Martin, Ryan, 2012. "Convergence rate for predictive recursion estimation of finite mixtures," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 378-384.
    6. Jingjing Wu & Rohana J. Karunamuni, 2018. "Efficient and robust tests for semiparametric models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 761-788, August.
    7. repec:bny:wpaper:0122 is not listed on IDEAS
    8. Xiang, Liming & Yau, Kelvin K.W. & Lee, Andy H., 2012. "The robust estimation method for a finite mixture of Poisson mixed-effect models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1994-2005.
    9. Wu, Jingjing & Karunamuni, Rohana & Zhang, Biao, 2010. "Minimum Hellinger distance estimation in a two-sample semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1102-1122, May.
    10. Karunamuni, Rohana J. & Wu, Jingjing, 2011. "One-step minimum Hellinger distance estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3148-3164, December.
    11. Wu, Jingjing & Karunamuni, Rohana J., 2012. "Efficient Hellinger distance estimates for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 1-23.
    12. Jingjing Wu & Tasnima Abedin & Qiang Zhao, 2023. "Semiparametric modelling of two-component mixtures with stochastic dominance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 39-70, February.
    13. Umashanger, T. & Sriram, T.N., 2009. "L2E estimation of mixture complexity for count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4243-4254, October.

    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:jmvana:v:101:y:2010:i:10:p:2411-2419. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.