IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v108y2013i503p914-928.html
   My bibliography  Save this article

Maximum L q -Likelihood Estimation via the Expectation-Maximization Algorithm: A Robust Estimation of Mixture Models

Author

Listed:
  • Yichen Qin
  • Carey E. Priebe

Abstract

We introduce a maximum L q -likelihood estimation (ML q E) of mixture models using our proposed expectation-maximization (EM) algorithm, namely the EM algorithm with L q -likelihood (EM-L q ). Properties of the ML q E obtained from the proposed EM-L q are studied through simulated mixture model data. Compared with the maximum likelihood estimation (MLE), which is obtained from the EM algorithm, the ML q E provides a more robust estimation against outliers for small sample sizes. In particular, we study the performance of the ML q E in the context of the gross error model, where the true model of interest is a mixture of two normal distributions, and the contamination component is a third normal distribution with a large variance. A numerical comparison between the ML q E and the MLE for this gross error model is presented in terms of Kullback--Leibler (KL) distance and relative efficiency.

Suggested Citation

  • Yichen Qin & Carey E. Priebe, 2013. "Maximum L q -Likelihood Estimation via the Expectation-Maximization Algorithm: A Robust Estimation of Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 914-928, September.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:914-928
    DOI: 10.1080/01621459.2013.787933
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2013.787933
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2013.787933?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.

    Citations

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


    Cited by:

    1. 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.
    2. Xu, Lin & Xiang, Sijia & Yao, Weixin, 2019. "Robust maximum Lq-likelihood estimation of joint mean–covariance models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 397-411.
    3. Yeşim Güney & Y. Tuaç & Ş. Özdemir & O. Arslan, 2021. "Conditional maximum Lq-likelihood estimation for regression model with autoregressive error terms," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 47-74, January.
    4. Nelson, Kenric P., 2022. "Independent Approximates enable closed-form estimation of heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).

    More about this item

    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:taf:jnlasa:v:108:y:2013:i:503:p:914-928. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.