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Two-sided bias bound of the Kaplan-Meier estimator
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  • Published: September 1988

Two-sided bias bound of the Kaplan-Meier estimator

  • M. Zhou1 

Probability Theory and Related Fields volume 79, pages 165–173 (1988)Cite this article

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  • 9 Citations

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Summary

We prove in this paper that the bias of the Kaplan-Meier estimator functional, which always under-estimates the true value, is decreasing at an exponential rate. An application of the inequality is also given.

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References

  • Aalen, O.: Nonparametric inference for a family of counting processes. Ann. Stat. 6, 701–726 (1978)

    MATH  MathSciNet  Google Scholar 

  • Breslow, N., Crowley, J.: A large sample study of the life table and product limit estimates under random censorship. Ann. Statist. 2, 437–453 (1974)

    MathSciNet  Google Scholar 

  • Chow, Y.S., Teicher, H.: Probability theory: independence, interchangeability, martingales. Berlin Heidelberg New York: Springer 1978

    Google Scholar 

  • Csörgő, S., Horváth, L.: The rate of strong uniform consistency for the product-limit estimator. Z. Wahrscheinlichkeitstheor. Verw. Geb. 62, 411–426 (1983)

    Google Scholar 

  • Földes, A., Rejtő, L.: A LIL type result for the product limit estimator. Z. Wahrscheinlichkeitstheor. Verw. Geb. 56, 75–86 (1980)

    Google Scholar 

  • Gill, R.: Censoring and stochastic integrals. Mathematical Centre Tracts 124. Amsterdam: Mathematisch Centrum 1980

    Google Scholar 

  • Gill, R.: Large sample behavior of the product-limit estimator on the whole line. Ann. Stat. 11, 49–58 (1983)

    MATH  MathSciNet  Google Scholar 

  • Kaplan, E., Meier, P.: Non-parametric estimator from incomplete observations. J. Am. Stat. Assoc. 53, 457–481 (1958)

    MathSciNet  Google Scholar 

  • Mauro, D.: A combinatoric approach to the Kaplan-Meier estimator. Ann. Stat. 13, 142–149 (1985)

    MATH  MathSciNet  Google Scholar 

  • Peterson, A.V.: Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions. J. Am. Stat. Assoc. 72, 845–858 (1977)

    Google Scholar 

  • Phadia, E.G., Van Ryzin, J.: A note on convergence rates for the product limit estimator. Ann. Stat. 8, 673–678 (1980)

    Google Scholar 

  • Susarla, V., Van Ryzin, J.: Large sample theory for an estimator of the mean survival time from censored samples. Ann. Stat. 8, 1002–1016 (1980)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    M. Zhou

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  1. M. Zhou
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Cite this article

Zhou, M. Two-sided bias bound of the Kaplan-Meier estimator. Probab. Th. Rel. Fields 79, 165–173 (1988). https://doi.org/10.1007/BF00320917

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  • Received: 01 June 1987

  • Revised: 07 March 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00320917

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Exponential Rate
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