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A maximum smoothed likelihood estimator in the current status continuous mark model

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  • Piet Groeneboom
  • Geurt Jongbloed
  • Birgit Witte

Abstract

We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark is only observed in case inspection takes place after the event time. The nonparametric maximum likelihood estimator in this model is known to be inconsistent. We propose and study an alternative likelihood-based estimator, maximising a smoothed log-likelihood, hence called a maximum smoothed likelihood estimator (MSLE). This estimator is shown to be well defined and consistent, and a simple algorithm is described that can be used to compute it. The MSLE is compared with other estimators in a small simulation study.

Suggested Citation

  • Piet Groeneboom & Geurt Jongbloed & Birgit Witte, 2012. "A maximum smoothed likelihood estimator in the current status continuous mark model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 85-101.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:85-101
    DOI: 10.1080/10485252.2011.621952
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    References listed on IDEAS

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    1. Marloes H. Maathuis & Jon A. Wellner, 2008. "Inconsistency of the MLE for the Joint Distribution of Interval‐Censored Survival Times and Continuous Marks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(1), pages 83-103, March.
    2. Michael G. Hudgens & Marloes H. Maathuis & Peter B. Gilbert, 2007. "Nonparametric Estimation of the Joint Distribution of a Survival Time Subject to Interval Censoring and a Continuous Mark Variable," Biometrics, The International Biometric Society, vol. 63(2), pages 372-380, June.
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    Cited by:

    1. Geurt Jongbloed & Frank H. van der Meulen & Lixue Pang, 2022. "Bayesian nonparametric estimation in the current status continuous mark model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1329-1352, September.

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    1. Geurt Jongbloed & Frank H. van der Meulen & Lixue Pang, 2022. "Bayesian nonparametric estimation in the current status continuous mark model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1329-1352, September.

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