Asymptotically efficient estimation of a survival function in the missing censoring indicator model

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Abstract

We propose and analyze a new estimator of a survival function in the random censorship model when the censoring indicator is missing at random for some study subjects. The proposed approach appeals to a known representation for the survival function, expressible as a smooth functional of a certain conditional probability and the cumulative hazard function of the observed minimum. Well-known estimators are substituted into this representation leading to a simple estimator of the survival function. The new estimator, whose asymptotic variance reduces to that of the Kaplan-Meier estimator when all the censoring indicators are observed, is shown to achieve the efficiency bound derived by van der Laan and McKeague.

Original languageEnglish (US)
Pages (from-to)797-817
Number of pages21
JournalJournal of Nonparametric Statistics
Volume16
Issue number5
DOIs
StatePublished - Oct 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Bandwidth sequence
  • Kernel density estimator
  • Limit theory
  • Mean integrated squared error
  • Reduced-data nonparametric maximum likelihood estimator
  • U-statistic

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