Berry-esseen bound for the kaplan-meier estimator

Abstract

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.

Keywords:

• Berry-Esseen bound
• Kaplan-Meier estimator
• U-statistics
• Empirical cumulative hazard
• Km cumulative hazard estimator