Comparison of the Kaplan-Meier and Nelson Estimators using Bootstrap Confidence Intervals

The bootstrap confidence intervals are a computer-based method for assigning measures of accuracy to statistical estimators. In this paper we examine the small sample behavior of the Kaplan-Meier and Nelson-type estimators for the survival function using the bootstrap and asymptotic normal-theory confidence intervals. The Nelson-type estimator is nearly always better than the Kaplan-Meier estimator in the sense of achieved error rates. From the point of confidence length, the reverse is true. Also, we show that the bootstrap confidence intervals are better than the asymptotic normal-theory confidence intervals in terms of achieved error rates and confidence length.