# The nonparametric bootstrap for the current status model

## TL;DR

This paper demonstrates that while direct bootstrap of the nonparametric MLE in the current status model is inconsistent, bootstrapping functionals of the MLE yields valid confidence intervals, supported by convergence results.

## Contribution

It introduces a method for valid bootstrap inference in the current status model by focusing on functionals of the MLE, overcoming previous inconsistency issues.

## Key findings

- Bootstrapped MLE converges at the correct rate in Lp-distance.
- Bootstrapping functionals of the MLE produces valid confidence intervals.
- Results extend to the current status regression model.

## Abstract

It has been proved that direct bootstrapping of the nonparametric maximum likelihood estimator (MLE) of the distribution function in the current status model leads to inconsistent confidence intervals. We show that bootstrapping of functionals of the MLE can however be used to produce valid intervals. To this end, we prove that the bootstrapped MLE converges at the right rate in the $L_p$-distance. We also discuss applications of this result to the current status regression model.