The performance of model based bootstrap methods for constructing point-wise confidence intervals around the survival function with interval censored data is investigated. It is shown that bootstrapping from the nonparametric maximum likelihood estimator of the survival function is inconsistent for the current status model. A model based smoothed bootstrap procedure is proposed and proved to be consistent. In fact, a general framework for proving the consistency of any model based bootstrap scheme in the current status model is established. In addition, simulation studies are conducted to illustrate the (in)-consistency of different bootstrap methods in mixed case interval censoring. The conclusions in the interval censoring model would extend more generally to estimators in regression models that exhibit non-standard rates of convergence.
Bibliographical noteFunding Information:
The authors thank the editor and the reviewers for their helpful comments. The first author gratefully acknowledges support from National Science Foundation grant DMS-1150435 .
- Consistency of bootstrap
- Current status data
- Mixed-case interval censoring
- Nonparametric maximum likelihood estimator