Bootstrapping the Kaplan-Meier Estimator on the Whole Line

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Abstract

This article is concerned with proving the consistency of Efron’s bootstrap for the Kaplan–Meier estimator on the whole support of a survival function. While previous works address the asymptotic Gaussianity of the Kaplan–Meier estimator without restricting time, we enable the construction of bootstrap-based time-simultaneous confidence bands for the whole survival function. Other practical applications include bootstrap-based confidence bands for the mean residual lifetime function or the Lorenz curve as well as confidence intervals for the Gini index. Theoretical results are complemented with a simulation study and a real data example which result in statistical recommendations.

Original languageEnglish
Pages (from-to)213-246
Number of pages34
JournalAnnals of the Institute of Statistical Mathematics
Volume71
Issue number1
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

  • Counting process
  • Efron’s bootstrap
  • Gini index
  • Lorenz curve
  • Mean residual lifetime
  • Resampling
  • Right censoring

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