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Berry-Esseen bound for the Kaplan-Meier estimator. (English) Zbl 0707.62079
The Berry-Esseen bound for U-statistics 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 the Kaplan- Meier estimator at a fixed time point t and the standard normal cumulative distribution function is bounded above by K(1+σ 1 -1 )[S(t)] -2 n -1/2 , where S(·) is the survival function and σ 1 is defined in the paper.

MSC:
62G05Nonparametric estimation
62G20Nonparametric asymptotic efficiency