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Consistency of the generalized MLE of a joint distribution function with multivariate interval-censored data

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  • Yu, Shaohua
  • Yu, Qiqing
  • Wong, George Y.C.

Abstract

Wong and Yu [Generalized MLE of a joint distribution function with multivariate interval-censored data, J. Multivariate Anal. 69 (1999) 155-166] discussed generalized maximum likelihood estimation of the joint distribution function of a multivariate random vector whose coordinates are subject to interval censoring. They established uniform consistency of the generalized MLE (GMLE) of the distribution function under the assumption that the random vector is independent of the censoring vector and that both of the vector distributions are discrete. We relax these assumptions and establish consistency results of the GMLE under a multivariate mixed case interval censorship model. van der Vaart and Wellner [Preservation theorems for Glivenko-Cantelli and uniform Glivenko-Cantelli class, in: E. Gine, D.M. Mason, J.A. Wellner (Eds.), High Dimensional Probability, vol. II, Birkhäuser, Boston, 2000, pp. 115-133] and Yu [Consistency of the generalized MLE with multivariate mixed case interval-censored data, Ph.D Dissertation, Binghamton University, 2000] independently proved strong consistency of the GMLE in the L1([mu])-topology, where [mu] is a measure derived from the joint distribution of the censoring variables. We establish strong consistency of the GMLE in the topologies of weak convergence and pointwise convergence, and eventually uniform convergence under appropriate distributional assumptions and regularity conditions.

Suggested Citation

  • Yu, Shaohua & Yu, Qiqing & Wong, George Y.C., 2006. "Consistency of the generalized MLE of a joint distribution function with multivariate interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 720-732, March.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:3:p:720-732
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    References listed on IDEAS

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    1. Jianguo Sun, 2003. "A nonparametric test for panel count data," Biometrika, Biometrika Trust, vol. 90(1), pages 199-208, March.
    2. Jian‐Jian Ren, 2003. "Goodness of fit tests with interval censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 211-226, March.
    3. Anton Schick & Qiqing Yu, 2000. "Consistency of the GMLE with Mixed Case Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 45-55, March.
    4. Yu, Qiqing & Schick, Anton & Li, Linxiong & Wong, George Y. C., 1998. "Asymptotic properties of the GMLE with case 2 interval-censored data," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 223-228, March.
    5. Wong, George Y. C. & Yu, Qiqing, 1999. "Generalized MLE of a Joint Distribution Function with Multivariate Interval-Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 155-166, May.
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    Cited by:

    1. Deng, Dianliang & Fang, Hong-Bin, 2009. "Asymptotics for non-parametric likelihood estimation with doubly censored multivariate failure times," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1802-1815, September.

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