Edgeworth expansions for the product-limit estimator under left-truncationand right-censoring with the bootstrap

An Edgeworth expansion for the distribution function of the product-limit e stimator of survival time under the left-truncation and right-censoring mod el is derived. This expansion gives more accurate approximations than the u sual normal approximation from weak convergence. In addition, by constructi ng the bootstrap sample from left-truncation and right-censored data, the E dgeworth expansion for the bootstrap statistic is given, allowing a bootstr ap base confidence interval with better coverage probability.