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A note on the asymptotic properties of the product-limit estimator on the whole line

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  • Ying, Zhiliang

Abstract

It was shown by Gill (1983) that a Donsker type theorem for empirical distributions holds for Kaplan-Meier estimates up to the point of last observation. In this note, we show that this restriction to last observation is unnecessary and convergence holds on the entire interval, providing a full extension of Donsker's result to censored models.

Suggested Citation

  • Ying, Zhiliang, 1989. "A note on the asymptotic properties of the product-limit estimator on the whole line," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 311-314, February.
    • Handle: RePEc:eee:stapro:v:7:y:1989:i:4:p:311-314
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    Citations

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    Cited by:

    1. He, Shuyuan & Yang, Grace L., 2000. "On the strong convergence of the product-limit estimator and its integrals under censoring and random truncation," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 235-244, September.
    2. Marija Cuparić & Bojana Milošević, 2022. "New characterization-based exponentiality tests for randomly censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 461-487, June.
    3. Valentin Patilea & Jean-Marc Rolin, 2004. "Product-limit Estimators of the Survival Function with Left or Right Censored Data," Working Papers 2004-36, Center for Research in Economics and Statistics.
    4. Qibing Gao & Xiuqing Zhou & Yanqin Feng & Xiuli Du & XiaoXiao Liu, 2021. "An empirical likelihood method for quantile regression models with censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 75-96, January.
    5. Valentin Patilea & Jean-Marie Rolin, 2004. "Product-Limit Estimators of the Survival Function with Twice Censored Data," Working Papers 2004-05, Center for Research in Economics and Statistics.
    6. Somnath Datta & Dipankar Bandyopadhyay & Glen A. Satten, 2010. "Inverse Probability of Censoring Weighted U‐statistics for Right‐Censored Data with an Application to Testing Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 680-700, December.
    7. Jean-Yves Dauxois & Agathe Guilloux, 2004. "Estimating the Cumulative incidence Functions under Length-biased Sampling," Working Papers 2004-01, Center for Research in Economics and Statistics.
    8. Dennis Dobler, 2019. "Bootstrapping the Kaplan–Meier estimator on the whole line," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 213-246, February.
    9. Dennis Dobler & Markus Pauly, 2018. "Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 639-658, September.
    10. Dauxois, Jean-Yves & Guilloux, Agathe, 2008. "Nonparametric inference under competing risks and selection-biased sampling," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 589-605, April.
    11. Yanqing Sun & Qiong Shou & Peter B. Gilbert & Fei Heng & Xiyuan Qian, 2023. "Semiparametric additive time‐varying coefficients model for longitudinal data with censored time origin," Biometrics, The International Biometric Society, vol. 79(2), pages 695-710, June.
    12. Lu Tian & Hua Jin & Hajime Uno & Ying Lu & Bo Huang & Keaven M. Anderson & LJ Wei, 2020. "On the empirical choice of the time window for restricted mean survival time," Biometrics, The International Biometric Society, vol. 76(4), pages 1157-1166, December.

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