The jackknife estimate of variance of a Kaplan-Meier integral. (English) Zbl 0878.62027

Summary: Let \(\widehat{F}_n\) be the Kaplan-Meier estimator of a distribution function \(F\) computed from randomly censored data. It is known that, under certain integrability assumptions on a function \(\varphi\), the Kaplan-Meier integral \(\int\varphi d\widehat{F}_n\), when properly standardized, is asymptotically normal. In this paper it is shown that, with probability 1, the jackknife estimate of variance consistently estimates the (limit) variance.


62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62G09 Nonparametric statistical resampling methods
62G30 Order statistics; empirical distribution functions
60G42 Martingales with discrete parameter


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