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 language | English |
|---|---|
| Pages (from-to) | 213-246 |
| Number of pages | 34 |
| Journal | Annals of the Institute of Statistical Mathematics |
| Volume | 71 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 |
| Externally published | Yes |
Funding
The author would like to thank Markus Pauly (Ulm University) for helpful discussions. Furthermore, the discussion with a referee and his / her suggestions to present numerical results and to illustrate the methods with the help of real data have helped to improve this manuscript significantly.
| Funders | Funder number |
|---|---|
| Universität Ulm |
Keywords
- Counting process
- Efron’s bootstrap
- Gini index
- Lorenz curve
- Mean residual lifetime
- Resampling
- Right censoring