The jackknife estimate of variance of a Kaplan-Meier integral

Abstract

Let F̂n 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 φ, the Kaplan-Meier integral ∫ φ dF̂n, 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.