The accuracy of normal approximations in censoring models
Paul Janssen, Noël Veraverbeke · Journal of nonparametric statistics · 1992
In a recent paper, Chang and Rao obtained a Berry-Esseen bound for the Kaplan-Meier estimator of the survival distribution in the general random censorship model. We complement their theorem by an analogous result for the ACL-estimator of the survival distribution in the proportional hazards model of random censorship. These rate of convergence results are used to obtain the accuracy of the normal approximations for estimators of quantiles of the survival time distribution in both of the censoring models. As a further application, we show how the U-statistic representations, implicitly contained in the proofs of the Berry-Esseen theorems for the estimators of the survival distribution, can be used to provide rate of convergence results for quantile estimators of the residual survival time distribution.