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Statistica Sinica 11(2001), 1069-1079



EDGEWORTH EXPANSIONS FOR THE PRODUCT-LIMIT

ESTIMATOR UNDER LEFT-TRUNCATION AND

RIGHT-CENSORING WITH THE BOOTSTRAP


Yi-Ting Hwang


Georgetown University School of Medicine


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, $\mathit{U}$-statistic.



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