IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i2p378-384.html
   My bibliography  Save this article

Convergence rate for predictive recursion estimation of finite mixtures

Author

Listed:
  • Martin, Ryan

Abstract

Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixing and mixture densities are consistent under fairly mild conditions, but currently very little is known about the rate of convergence. Here I first investigate asymptotic convergence properties of the PR estimate under model misspecification in the special case of finite mixtures with known support. Tools from stochastic approximation theory are used to prove that the PR estimates converge, to the best Kullback–Leibler approximation, at a nearly root-n rate. When the support is unknown, PR can be used to construct an objective function which, when optimized, yields an estimate of the support. I apply the known-support results to derive a rate of convergence for this modified PR estimate in the unknown support case, which compares favorably to known optimal rates.

Suggested Citation

  • Martin, Ryan, 2012. "Convergence rate for predictive recursion estimation of finite mixtures," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 378-384.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:378-384
    DOI: 10.1016/j.spl.2011.10.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211003440
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2011.10.023?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. Ishwaran H. & James L.F. & Sun J., 2001. "Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1316-1332, December.
    2. Ryan Martin & Surya T. Tokdar, 2011. "Semiparametric inference in mixture models with predictive recursion marginal likelihood," Biometrika, Biometrika Trust, vol. 98(3), pages 567-582.
    3. 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.
    4. Chen, Jiahua & Khalili, Abbas, 2008. "Order Selection in Finite Mixture Models With a Nonsmooth Penalty," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1674-1683.
    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. Ryan Martin, 2021. "A Survey of Nonparametric Mixing Density Estimation via the Predictive Recursion Algorithm," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 97-121, May.

    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. 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.
    2. Aßmann, Christian & Boysen-Hogrefe, Jens, 2009. "A bayesian approach to model-based clustering for panel probit models," Economics Working Papers 2009-03, Christian-Albrechts-University of Kiel, Department of Economics.
    3. Aßmann, Christian & Boysen-Hogrefe, Jens, 2011. "A Bayesian approach to model-based clustering for binary panel probit models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 261-279, January.
    4. Zhiqiang Zheng & Balaji Padmanabhan, 2007. "Constructing Ensembles from Data Envelopment Analysis," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 486-496, November.
    5. Zhan, Tingting & Chevoneva, Inna & Iglewicz, Boris, 2011. "Generalized weighted likelihood density estimators with application to finite mixture of exponential family distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 457-465, January.
    6. 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.
    7. Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 816-832, April.
    8. Florian Huber & Tam'as Krisztin & Michael Pfarrhofer, 2018. "A Bayesian panel VAR model to analyze the impact of climate change on high-income economies," Papers 1804.01554, arXiv.org, revised Feb 2021.
    9. 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.
    10. Sandra Fortini & Sonia Petrone, 2020. "Quasi‐Bayes properties of a procedure for sequential learning in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 1087-1114, September.
    11. David A. Spade, 2020. "Geometric ergodicity of a Metropolis-Hastings algorithm for Bayesian inference of phylogenetic branch lengths," Computational Statistics, Springer, vol. 35(4), pages 2043-2076, December.
    12. 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.
    13. 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.
    14. 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.
    15. Antoine Chambaz & Judith Rousseau, 2005. "Nonasymptotic Bounds for Bayesian Order Identification with Application to Mixtures," Working Papers 2005-27, Center for Research in Economics and Statistics.
    16. Huber, Florian, 2018. "Dealing with heterogeneity in panel VARs using sparse finite mixtures," Department of Economics Working Paper Series 262, WU Vienna University of Economics and Business.
    17. 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.
    18. Juarez, Miguel A. & Steel, Mark F. J., 2006. "Model-based Clustering of non-Gaussian Panel Data," MPRA Paper 880, University Library of Munich, Germany.
    19. Xu, Peirong & Peng, Heng & Huang, Tao, 2018. "Unsupervised learning of mixture regression models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 44-56.
    20. 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.

    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:stapro:v:82:y:2012:i:2:p:378-384. 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.