IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/30481.html
   My bibliography  Save this paper

Parameter recovery in two-component contamination mixtures: the L2 strategy

Author

Listed:
  • Gadat, Sébastien
  • Marteau, Clément
  • Maugis, Cathy

Abstract

In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, f* = (1 - lambda*)phi + lambda*phi (. - mu*), where the shape phi is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters (lambda*, mu*) is an element of (0, 1) x R-d. In particular, we prove that the classical parametric rate 1/ root n cannot be reached when at least one of these parameters is allowed to tend to 0 with n.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
    • Handle: RePEc:tse:wpaper:30481
    as

    Download full text from publisher

    File URL: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2016/wp_tse_653.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cristina Butucea & Pierre Vandekerkhove, 2014. "Semiparametric Mixtures of Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 227-239, March.
    2. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.
    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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. De Castro, Y. & Gadat, Sébastien & Marteau, Clément & Maugis, Cathy, 2019. "SuperMix: Sparse Regularization for Mixture," TSE Working Papers 19-1040, Toulouse School of Economics (TSE), revised Sep 2020.

    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. 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.
    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. 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.
    4. Marc Henry & Koen Jochmans & Bernard Salanié, 2014. "Inference on Mixtures Under Tail Restrictions," SciencePo Working papers Main hal-01053810, HAL.
    5. 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.
    6. repec:hal:spmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS
    7. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Estimating Multivariate Latent-Structure Models," SciencePo Working papers Main hal-01097135, HAL.
    8. Rostyslav Maiboroda & Olena Sugakova, 2012. "Nonparametric density estimation for symmetric distributions by contaminated data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 109-126, January.
    9. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    10. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    11. De Castro, Y. & Gadat, Sébastien & Marteau, Clément & Maugis, Cathy, 2019. "SuperMix: Sparse Regularization for Mixture," TSE Working Papers 19-1040, Toulouse School of Economics (TSE), revised Sep 2020.
    12. Chauveau, Didier & Hoang, Vy Thuy Lynh, 2016. "Nonparametric mixture models with conditionally independent multivariate component densities," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 1-16.
    13. Wu, Jingjing & Karunamuni, Rohana J., 2012. "Efficient Hellinger distance estimates for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 1-23.
    14. 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.
    15. Xiaotian Zhu & David R. Hunter, 2019. "Clustering via finite nonparametric ICA mixture models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 65-87, March.
    16. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.
    17. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p2m96cphi is not listed on IDEAS
    18. Yuichi Kitamura & Louise Laage, 2018. "Nonparametric Analysis of Finite Mixtures," Papers 1811.02727, arXiv.org.
    19. Xiang, Sijia & Yao, Weixin & Seo, Byungtae, 2016. "Semiparametric mixture: Continuous scale mixture approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 413-425.
    20. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, March.
    21. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m96cphi is not listed on IDEAS
    22. Cristina Butucea & Pierre Vandekerkhove, 2014. "Semiparametric Mixtures of Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 227-239, March.
    23. Domma, Filippo & Condino, Francesca, 2014. "A new class of distribution functions for lifetime data," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 36-45.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tse:wpaper:30481. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    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.