IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v95y2014icp144-149.html
   My bibliography  Save this article

On location mixtures with Pólya frequency components

Author

Listed:
  • Balabdaoui, Fadoua
  • Butucea, Cristina

Abstract

We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X0 with a certain probability. We show that if X0 admits a density that is a Pólya frequency function with E[X0]=0, then k, a1,…,ak and π1,…,πk are identifiable for any k≥1. We discuss how log-concave maximum likelihood can be used to estimate the mixed and the unknown density f0 when the latter is symmetric.

Suggested Citation

  • Balabdaoui, Fadoua & Butucea, Cristina, 2014. "On location mixtures with Pólya frequency components," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 144-149.
    • Handle: RePEc:eee:stapro:v:95:y:2014:i:c:p:144-149
    DOI: 10.1016/j.spl.2014.08.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214002922
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.08.013?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. Chang, George T. & Walther, Guenther, 2007. "Clustering with mixtures of log-concave distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6242-6251, August.
    2. Christian Hennig & Tim F. Liao, 2013. "How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 309-369, May.
    3. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
    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. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    2. Hu, Hao & Wu, Yichao & Yao, Weixin, 2016. "Maximum likelihood estimation of the mixture of log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 137-147.
    3. Pietro Coretto & Christian Hennig, 2016. "Robust Improper Maximum Likelihood: Tuning, Computation, and a Comparison With Other Methods for Robust Gaussian Clustering," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1648-1659, October.
    4. Marc Henry & Koen Jochmans & Bernard Salanié, 2014. "Inference on Mixtures Under Tail Restrictions," SciencePo Working papers Main hal-01053810, HAL.
    5. Wu, Jingjing & Karunamuni, Rohana J., 2012. "Efficient Hellinger distance estimates for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 1-23.
    6. Morgan, Grant B. & Hodge, Kari J. & Baggett, Aaron R., 2016. "Latent profile analysis with nonnormal mixtures: A Monte Carlo examination of model selection using fit indices," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 146-161.
    7. Elvira Pelle & Roberta Pappadà, 2021. "A clustering procedure for mixed-type data to explore ego network typologies: an application to elderly people living alone in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1507-1533, December.
    8. Seo, Byungtae, 2017. "The doubly smoothed maximum likelihood estimation for location-shifted semiparametric mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 27-39.
    9. Jack Blundell, 2020. "Clusters in UK Self-Employment," CEP Occasional Papers 048, Centre for Economic Performance, LSE.
    10. Brittney Goodrich & Jisang Yu & Monte Vandeveer, 2020. "Participation patterns of the rainfall index insurance for pasture, rangeland and forage programme," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(1), pages 29-51, January.
    11. Roberto Mari & Roberto Rocci & Stefano Antonio Gattone, 2020. "Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 49-78, March.
    12. Gadat, Sébastien & Marteau, Clément & Maugis, Cathy, 2016. "Parameter recovery in two-component contamination mixtures: the L2 strategy," TSE Working Papers 16-653, Toulouse School of Economics (TSE), revised Feb 2018.
    13. Mu, Xiaosheng, 2015. "Log-concavity of a mixture of beta distributions," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 125-130.
    14. Fernández, D. & Arnold, R. & Pledger, S., 2016. "Mixture-based clustering for the ordered stereotype model," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 46-75.
    15. Layal Christine Lettry, 2023. "Clustering the Swiss Pension Register," FSES Working Papers 529, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    16. Jiali Zheng & Xiyang Wang, 2022. "Estimation for a Class of Semiparametric Pareto Mixture Densities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 609-627, August.
    17. Goodrich, Brittney K. & Goodhue, Rachael E., 2020. "Are All Colonies Created Equal? The Role of Honey Bee Colony Strength in Almond Pollination Contracts," Ecological Economics, Elsevier, vol. 177(C).
    18. Marcel Raab & Anette Fasang & Aleksi Karhula & Jani Erola, 2014. "Sibling Similarity in Family Formation," Demography, Springer;Population Association of America (PAA), vol. 51(6), pages 2127-2154, December.
    19. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2016. "Non-parametric estimation of finite mixtures from repeated measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 211-229, January.
    20. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "Erratum to: The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 327-355, July.

    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:95:y:2014:i:c:p:144-149. 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.