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Semiparametric models: a generalized self‐consistency approach

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  • 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
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    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.

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