An Estimator for the Survival Function on the Basis of Observable Censoring Times

Abstract

Chiu [Chiu, S. N. (1999). An unbiased estimator for the survival function of censored data. Commun. Statist. - Theory Meth. 28(9):2249–2260.] proposed a nonparametric estimator for the survival function which is based on observable censoring times in the general censoring model. His estimator is less efficient than the Product-Limit estimator. Considering an informative censoring model this drawback can partially be overcome. This is shown by a nonparametric, uniformly consistent estimator based on observable censoring times within the simple Koziol–Green model. Some asymptotic properties of the new estimator are investigated and it is compared with the well-known ACL-estimator.

Keywords:

• Nonparametric survival curve estimator
• Informative random censoring
• Koziol–Green model
• ACL-estimator