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Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator
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  • Published: September 1989

Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator

  • S. H. Lo1,
  • Y. P. Mack2 &
  • J. L. Wang2 

Probability Theory and Related Fields volume 80, pages 461–473 (1989)Cite this article

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Summary

We study the estimation of a density and a hazard rate function based on censored data by the kernel smoothing method. Our technique is facilitated by a recent result of Lo and Singh (1986) which establishes a strong uniform approximation of the Kaplan-Meier estimator by an average of independent random variables. (Note that the approximation is carried out on the original probability space, which should be distinguished from the Hungarian embedding approach.) Pointwise strong consistency and a law of iterated logarithm are derived, as well as the mean squared error expression and asymptotic normality, which is obtain using a more traditional method, as compared with the Hajek projection employed by Tanner and Wong (1983).

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Authors and Affiliations

  1. Department of Statistics, Harvard University, 02138, Cambridge, MA, USA

    S. H. Lo

  2. Division of Statistics, University of California, 95616, Davis, CA, USA

    Y. P. Mack & J. L. Wang

Authors
  1. S. H. Lo
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  2. Y. P. Mack
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  3. J. L. Wang
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Lo, S.H., Mack, Y.P. & Wang, J.L. Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator. Probab. Th. Rel. Fields 80, 461–473 (1989). https://doi.org/10.1007/BF01794434

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  • Received: 01 November 1986

  • Revised: 10 May 1988

  • Issue Date: September 1989

  • DOI: https://doi.org/10.1007/BF01794434

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Keywords

  • Mathematical Biology
  • Hazard Rate
  • Rate Estimation
  • Independent Random Variable
  • Asymptotic Normality
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