The wild bootstrap for multivariate Nelson–Aalen estimators

Tobias Bluhmki, Dennis Dobler*, Jan Beyersmann, Markus Pauly

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


We rigorously extend the widely used wild bootstrap resampling technique to the multivariate Nelson–Aalen estimator under Aalen’s multiplicative intensity model. Aalen’s model covers general Markovian multistate models including competing risks subject to independent left-truncation and right-censoring. This leads to various statistical applications such as asymptotically valid confidence bands or tests for equivalence and proportional hazards. This is exemplified in a data analysis examining the impact of ventilation on the duration of intensive care unit stay. The finite sample properties of the new procedures are investigated in a simulation study.

Original languageEnglish
Pages (from-to)97-127
Number of pages31
JournalLifetime data analysis
Issue number1
Early online date6 Mar 2018
Publication statusPublished - 15 Jan 2019


  • Conditional central limit theorem
  • Counting process
  • Equivalence test
  • Kolmogorov–Smirnov test
  • Proportional hazards
  • Survival analysis
  • Weak convergence


Dive into the research topics of 'The wild bootstrap for multivariate Nelson–Aalen estimators'. Together they form a unique fingerprint.

Cite this