Abstract: In this paper, the asymptotic accuracies of the one-term Edgeworth expansions and the smoothed bootstrap approximation for the studentized Kaplan-Meier (KM) estimato r are investigated, respectively. It is shown that the Edgeworth expansions and the smoothed bootstrap approximation are asymptotically close to the exact distribution of the KM estimator with a remainder o(n-1/2) under some mild conditions. A simulation study has been used to compare the asymptotic performance of the Edgeworth expansion with that of smoothed bootstrap and unsmoothed bootstrap.
Key words and phrases: Asymptotic normality, asymptotic representation, asymptotic variance, Edgeworth expansion, Jackknife estimator, studentized Kaplan-Meier estimator.