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Nonparametric estimation of the bivariate survival function for one modified form of doubly censored data

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Abstract

In this article, we consider estimating the bivariate distribution function when both components are subject to double censoring. We propose three types of estimators, the first two are generalizations of the Dabrowska and Campbell and Földes estimators, and the third is an inverse-probability-weighted estimator. The consistency of the proposed estimators is established. A simulation study is conducted to investigate the performance of the proposed estimators.

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References

  • Campbell G, Földes A (1982) Large sample properties of nonparametric statistical inference. In: Gnredenko BV, Puri ML, Vineze I(eds) Nonparametric statistical inference. North-Holland, Amsterdam, pp 103–122

    Google Scholar 

  • Chang MN, Yang GL (1987) Strong consistency of a nonparametric estimator of the survival function with doubly censored data. Ann Statist 15: 1536–1547

    Article  MATH  MathSciNet  Google Scholar 

  • Dabrowska DM (1988) Kaplan–Meier estimate on the plane. Ann Statist 18: 1475–1489

    Article  MathSciNet  Google Scholar 

  • Dabrowska DM (1989) Kaplan–Meier estimate on the plane: weak convergence, LIL, and the bootstrap. J Multivar Anal 29: 308–325

    Article  MATH  MathSciNet  Google Scholar 

  • Gill RD, van der Laan MJ, Wellner JA (1995) Inefficient estimators of the bivariate survival function for three models. Annales de l’Institut Henri Poincare Section B: Calcul des Probabilite et Statistique 31: 547–597

    Google Scholar 

  • Gross ST, Lai TL (1996) Bootstrap methods for truncated censored data. Statistica Sinica 6: 509–530

    MATH  MathSciNet  Google Scholar 

  • Gu MG, Zhang CH (1993) Asymptotic properties of self-consistent estimators based on doubly censored data. Ann Statist 21: 611–624

    Article  MATH  MathSciNet  Google Scholar 

  • Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Amer Statist Assoc 53: 457–481

    Article  MATH  MathSciNet  Google Scholar 

  • Mykland PA, Ren J (1996) Algorithms for computing self-consistent and maximum likelihood estimators with doubly censored data. Ann Statist 24: 1740–1764

    Article  MATH  MathSciNet  Google Scholar 

  • Prentice RL, Cai J (1992) Covariance and survivor funciton estimation using censored multivariate failure time data. Biometrika 79: 495–512

    Article  MATH  MathSciNet  Google Scholar 

  • Ren J, Gu M (1997) Regression M-estimators with doubly censored data. Ann Statist 25: 2638–2664

    Article  MATH  MathSciNet  Google Scholar 

  • Robins JM (1993) Information recovery and bias adjustment in proportional hazards regression analysis of randomized trials using surrogate markers. In: Proceedings of the American Statistical Association- Biopharmaceutical Section, Alexaandria, VA: ASA, pp. 24–33

  • Robins JM, Finkelstein D (2000) Correcting for non-compliance and dependent censoring in an AIDS clinical trial with inverse probability of censoring weighted (IPCW) log-rank tests. Biometrices 56: 779–788

    Article  MATH  Google Scholar 

  • Satten GA, Datta S (2001) The Kaplan-Meier estimator as an inverse-probability-of-censoring weighted average. Amer Statist Ass 55: 207–210

    Article  MATH  MathSciNet  Google Scholar 

  • Tsai WY, Crowley J (1985) A large sample study of generalized maximum likelihood estimators from incomplete data via self-consistency. Ann Statist 13: 1317–1334

    Article  MATH  MathSciNet  Google Scholar 

  • van der Vaart AW, Wellner JA (2000) Weak convergence and empirical processes (with application to statistics). Springer Series in statistics

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Authors and Affiliations

  1. Department of Statistics, Tunghai university, Taichung, 40704, Taiwan

    Pao-sheng Shen

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  1. Pao-sheng Shen
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Correspondence to Pao-sheng Shen.

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Shen, Ps. Nonparametric estimation of the bivariate survival function for one modified form of doubly censored data. Comput Stat 25, 203–213 (2010). https://doi.org/10.1007/s00180-009-0171-y

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  • DOI: https://doi.org/10.1007/s00180-009-0171-y

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