The Kaplan-Meier estimator and hazard estimator for censored END survival time observations

摘要

In this paper, the survival function and hazard rate estimator by the Kaplan-Meier method are considered, where the survival times and censoring times are two sequences of extended negatively dependent. Under some suitable conditions, the uniform strong approximation rates for the survival function and hazard rate estimator are established with the rate O(n(-1/2) log(1/2n)) a.s., also, their strong representations are obtained with a remainder O(n(-1/2) log(1/2)n) a.s. Our results generalize and extend the corresponding ones in the related literatures.