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Asymptotics for non-parametric likelihood estimation with doubly censored multivariate failure times

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  • Deng, Dianliang
  • Fang, Hong-Bin

Abstract

This paper considers non-parametric estimation of a multivariate failure time distribution function when only doubly censored data are available, which occurs in many situations such as epidemiological studies. In these situations, each of multivariate failure times of interest is defined as the elapsed time between an initial event and a subsequent event and the observations on both events can suffer censoring. As a consequence, the estimation of multivariate distribution is much more complicated than that for multivariate right- or interval-censored failure time data both theoretically and practically. For the problem, although several procedures have been proposed, they are only ad-hoc approaches as the asymptotic properties of the resulting estimates are basically unknown. We investigate both the consistency and the convergence rate of a commonly used non-parametric estimate and show that as the dimension of multivariate failure time increases or the number of censoring intervals of multivariate failure time decreases, the convergence rate for non-parametric estimate decreases, and is slower than that with multivariate singly right-censored or interval-censored data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1802-1815
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    References listed on IDEAS

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    1. R. B. Geskus & P. Groeneboom, 1997. "Asymptotically optimal estimation of smooth functionals for interval censoring, part 2," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(2), pages 201-219, July.
    2. Komarek, Arnost & Lesaffre, Emmanuel, 2008. "Bayesian Accelerated Failure Time Model With Multivariate Doubly Interval-Censored Data and Flexible Distributional Assumptions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 523-533, June.
    3. 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.
    4. 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.
    5. William B. Goggins & Dianne M. Finkelstein, 2000. "A Proportional Hazards Model for Multivariate Interval-Censored Failure Time Data," Biometrics, The International Biometric Society, vol. 56(3), pages 940-943, September.
    6. Fang, Hong-Bin & Sun, Jianguo, 2001. "Consistency of nonparametric maximum likelihood estimation of a distribution function based on doubly interval-censored failure time data," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 311-318, December.
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