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Asymptotic theory for estimators under random censorship
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  • Published: June 1991

Asymptotic theory for estimators under random censorship

  • Gutti Jogesh Babu1 

Probability Theory and Related Fields volume 90, pages 275–290 (1991)Cite this article

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Summary

The product limit estimator\(\hat F\) of an unknown distributionF is represented as aU-statistic plus an error of the ordero(1/n). Using this, the maximum likelihood estimator of the specific risk rate in the time interval [0,M], is shown to admit a two term Edgeworth expansion. This risk rate for a specific cause of death is defined as the ratio of the probability of death, due to that particular cause, in the time interval [0,M], to the mean life time of an individual up to that time pointM. Similar expansions for the bootstrapped statistics are used to show that the bootstrap distribution, of the studentized estimator of the risk rate, approximates the sampling distribution better than the corresponding normal distribution.

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Author information

Authors and Affiliations

  1. Department of Statistics, 219 Pond Laboratory, The Pennsylvania State University, 16802, University Park, PA, USA

    Gutti Jogesh Babu

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  1. Gutti Jogesh Babu
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Additional information

Research supported in part by NSA Grant MDA 904-90-H-1001 and by NSF Grant DMS-9007717

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Cite this article

Babu, G.J. Asymptotic theory for estimators under random censorship. Probab. Th. Rel. Fields 90, 275–290 (1991). https://doi.org/10.1007/BF01192165

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  • Received: 04 April 1990

  • Revised: 15 April 1991

  • Issue Date: June 1991

  • DOI: https://doi.org/10.1007/BF01192165

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Keywords

  • Normal Distribution
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Life Time
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