IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v131y2014icp51-64.html
   My bibliography  Save this article

Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples

Author

Listed:
  • El-Dakkak, Omar
  • Peccati, Giovanni
  • Prünster, Igor

Abstract

We study Hoeffding decomposable exchangeable sequences with values in a finite set D={d1,…,dK}. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K≥3, there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable.

Suggested Citation

  • El-Dakkak, Omar & Peccati, Giovanni & Prünster, Igor, 2014. "Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 51-64.
    • Handle: RePEc:eee:jmvana:v:131:y:2014:i:c:p:51-64
    DOI: 10.1016/j.jmva.2014.04.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14000955
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.04.012?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. Vitale, Richard A., 1992. "Covariances of symmetric statistics," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 14-26, April.
    2. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 105-120, March.
    Full references (including those not matched with items 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. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    2. Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.
    3. Canale, Antonio & Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2023. "Inner spike and slab Bayesian nonparametric models," Econometrics and Statistics, Elsevier, vol. 27(C), pages 120-135.
    4. 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.
    5. Federico Zincenko, 2023. "Nonparametric estimation of conditional densities by generalized random forests," Papers 2309.13251, arXiv.org, revised May 2024.
    6. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 686-701.
    7. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97, March.
    8. James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Luai Al Labadi & Ibrahim Abdelrazeq, 2017. "On functional central limit theorems of Bayesian nonparametric priors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 215-229, June.
    10. Collet, Francesca & Leisen, Fabrizio, 2011. "Free completely random measures," DES - Working Papers. Statistics and Econometrics. WS ws112821, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
    12. Lachièze-Rey, Raphaël & Peccati, Giovanni, 2013. "Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric U-statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4186-4218.
    13. Rempala, Grzegorz, 1998. "Strong law of large numbers for U-statistics of varying order," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 263-270, August.
    14. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    15. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    16. J. E. Griffin & M. Kolossiatis & M. F. J. Steel, 2013. "Comparing distributions by using dependent normalized random-measure mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 499-529, June.
    17. Antonio Lijoi & Bernardo Nipoti & Igor Prünster, 2013. "Dependent mixture models: clustering and borrowing information," DEM Working Papers Series 046, University of Pavia, Department of Economics and Management.
    18. Ali Karimnezhad & Mahmoud Zarepour, 2020. "A general guide in Bayesian and robust Bayesian estimation using Dirichlet processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 321-346, April.
    19. Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2014. "Dependent mixture models: Clustering and borrowing information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 417-433.
    20. Stefano Favaro & Antonio Lijoi & Igor Prunster, 2011. "Asymptotics for a Bayesian nonparametric estimator of species richness," Quaderni di Dipartimento 144, University of Pavia, Department of Economics and Quantitative Methods.

    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:131:y:2014:i:c:p:51-64. 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.