Abstract
For left-truncated and right-censored data, the product-limit estimator Fˆxis a well-known nonparametric estimator for the distribution function Fx of the target variable X such as the survival time. Since Fˆxas a very complicated product form we establish first the Berry-Esseen bound for the cumulative hazard estimator of Fx The cumulative hazard estimator can be represented as a U-statistic. By using the result in Helmers and van Zwet [6], we derive the Berry-esséen bound for this U-statistic. Then Berry-Esseen bounds for the distribution of the cumulative hazard estimator and the normal distribution and the distribution of the product-limit estimator and the normal distribution are obtained.