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The Berry-Esseen bound for U-statistics, established by Helmers and Van Zwet (1982), is combined with the Breslow-Crowley (1974) bounds for the difference between the empirical cumulative hazard and the Kaplan-Meier cumulative hazard estimators of the survival function to derive a Berry-Esseen bound for the Kaplan-Meier estimator. We show that there exists an absolute quantity K such that the absolute difference between the standardized distribution function of Kaplan-Meier estimator at a fixed time point t and the standard normal cumulative distribution function is bounded above by where S(·) is the survival function and σ1is defined in Lemma 1.
Chang et al. (Sun,) studied this question.
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