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Inconsistency of the MLE for the Joint Distribution of Interval‐Censored Survival Times and Continuous Marks

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  • MARLOES H. MAATHUIS
  • JON A. WELLNER

Abstract

. This paper considers the non‐parametric maximum likelihood estimator (MLE) for the joint distribution function of an interval‐censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this problem. We use this formula and the mark‐specific cumulative hazard function of Huang & Louis (1998) to obtain the almost sure limit of the MLE. This result leads to necessary and sufficient conditions for consistency of the MLE, which imply that the MLE is inconsistent in general. We show that the inconsistency can be repaired by discretizing the marks. Our theoretical results are supported by simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:1:p:83-103
    DOI: 10.1111/j.1467-9469.2007.00568.x
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    Cited by:

    1. 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.
    2. 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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