Abstract: An Edgeworth expansion for the distribution function of the product-limit estimator of survival time under the left-truncation and right-censoring model is derived. This expansion gives more accurate approximations than the usual normal approximation from weak convergence. In addition, by constructing the bootstrap sample from left-truncation and right-censored data, the Edgeworth expansion for the bootstrap statistic is given, allowing a bootstrap base confidence interval with better coverage probability.
Key words and phrases: Bootstrap, censoring, edgeworth expansion, truncation, U-statistic.