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A semiparametric model for truncated and censored data

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  • Sun, Liuquan
  • Zhu, Lixing

Abstract

In this paper we propose and study a semiparametric estimator of the survival function based on left truncated and right censored data. Uniform consistency and a functional central limit result for this estimator are established. In addition, this estimator is shown to be superior to the product-limit estimator in terms of asymptotic variance.

Suggested Citation

  • Sun, Liuquan & Zhu, Lixing, 2000. "A semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 217-227, July.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:3:p:217-227
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    References listed on IDEAS

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    1. Arcones, Miguel A. & Giné, Evarist, 1995. "On the law of the iterated logarithm for canonical U-statistics and processes," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 217-245, August.
    2. Alexander, Kenneth S. & Talagrand, Michel, 1989. "The law of the iterated logarithm for empirical processes on Vapnik-Cervonenkis classes," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 155-166, July.
    3. Zhou, Yong, 1996. "A note on the TJW product-limit estimator for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 381-387, March.
    4. Cheng, Philip E. & Lin, Gwo Dong, 1987. "Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 75-80, January.
    5. Gijbels, I. & Wang, J. L., 1993. "Strong Representations of the Survival Function Estimator for Truncated and Censored Data with Applications," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 210-229, November.
    6. W. Stute, 1992. "Strong consistency of the MLE under random censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 39(1), pages 257-267, December.
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    Cited by:

    1. Dikta, Gerhard, 2014. "Asymptotically efficient estimation under semi-parametric random censorship models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 10-24.
    2. Austin, Matthew D. & Betensky, Rebecca A., 2014. "Eliminating bias due to censoring in Kendall’s tau estimators for quasi-independence of truncation and failure," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 16-26.
    3. Subramanian, Sundarraman & Bandyopadhyay, Dipankar, 2008. "Semiparametric left truncation and right censorship models with missing censoring indicators," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2572-2577, November.
    4. Sun, Liuquan, 2006. "The strong law under a semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1550-1558, August.
    5. Micha Mandel & Rebecca A. Betensky, 2007. "Testing Goodness of Fit of a Uniform Truncation Model," Biometrics, The International Biometric Society, vol. 63(2), pages 405-412, June.

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