Summary: The problem of sufficiently precise confidence interval estimation in the Koziol-Green or proportional hazards random censorship model is considered. Sequential procedures based on the Abdushukurov-Cheng-Lin estimate [see P. E. Cheng and G. D. Lin, Stat. Probab. Lett. 5, 75-80 (1987; Zbl 0629.62096)] are proposed to solve the problem. The procedures are shown to yield the desired degree of precision and desired confidence, asymptotically as one requires more and more precision. They are also asymptotically efficient with respect to sample size.
The limiting distribution of the sample size, and a second order expansion for its expected value, are obtained. Simulation results show that the procedure performs well and in particular that it does substantial better (when the Koziol-Green model holds) than an analogous procedure based on the Kaplan-Meier estimate. Results are also given that provide sufficiently precise confidence bands for the entire survival function.