IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v65y2003i3p759-774.html
   My bibliography  Save this article

Semiparametric models: a generalized self‐consistency approach

Author

Listed:
  • A. Tsodikov

Abstract

Summary. In semiparametric models, the dimension d of the maximum likelihood problem is potentially unlimited. Conventional estimation methods generally behave like O(d3). A new O(d) estimation procedure is proposed for a large class of semiparametric models. Potentially unlimited dimension is handled in a numerically efficient way through a Nelson–Aalen‐like estimator. Discussion of the new method is put in the context of recently developed minorization–maximization algorithms based on surrogate objective functions. The procedure for semiparametric models is used to demonstrate three methods to construct a surrogate objective function: using the difference of two concave functions, the EM way and the new quasi‐EM (QEM) approach. The QEM approach is based on a generalization of the EM‐like construction of the surrogate objective function so it does not depend on the missing data representation of the model. Like the EM algorithm, the QEM method has a dual interpretation, a result of merging the idea of surrogate maximization with the idea of imputation and self‐consistency. The new approach is compared with other possible approaches by using simulations and analysis of real data. The proportional odds model is used as an example throughout the paper.

Suggested Citation

  • A. Tsodikov, 2003. "Semiparametric models: a generalized self‐consistency approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 759-774, August.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:3:p:759-774
    DOI: 10.1111/1467-9868.00414
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00414
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00414?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
    ---><---

    Citations

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


    Cited by:

    1. Qui Tran & Kelley M. Kidwell & Alex Tsodikov, 2018. "A joint model of cancer incidence, metastasis, and mortality," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 385-406, July.
    2. John Dixon & Michael Kosorok & Bee Lee, 2005. "Functional inference in semiparametric models using the piggyback bootstrap," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 255-277, June.
    3. John D. Rice & Alex Tsodikov, 2017. "Semiparametric time-to-event modeling in the presence of a latent progression event," Biometrics, The International Biometric Society, vol. 73(2), pages 463-472, June.
    4. López-Cheda, Ana & Cao, Ricardo & Jácome, M. Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 144-165.
    5. Rebafka Tabea & Roueff François & Souloumiac Antoine, 2010. "A Corrected Likelihood Approach for the Nonlinear Transformation Model with Application to Fluorescence Lifetime Measurements Using Exponential Mixtures," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-34, March.
    6. Gressani, Oswaldo & Lambert, Philippe, 2016. "Fast Bayesian inference in semi-parametric P-spline cure survival models using Laplace approximations," LIDAM Discussion Papers ISBA 2016041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Lopez-Cheda , Ana & Cao, Ricardo & Jacome, Maria Amalia & Van Keilegom, Ingrid, 2015. "Nonparametric incidence and latency estimation in mixture cure models," LIDAM Discussion Papers ISBA 2015014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Gressani, Oswaldo & Lambert, Philippe, 2018. "Fast Bayesian inference using Laplace approximations in a flexible promotion time cure model based on P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 151-167.
    9. Muller, Ursula & Van Keilegom, Ingrid, 2016. "Goodness-of-t tests for the cure rate in a mixture cure model," LIDAM Discussion Papers ISBA 2016037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Ana Ezquerro & Brais Cancela & Ana López-Cheda, 2023. "On the Reliability of Machine Learning Models for Survival Analysis When Cure Is a Possibility," Mathematics, MDPI, vol. 11(19), pages 1-21, October.

    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:bla:jorssb:v:65:y:2003:i:3:p:759-774. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.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.