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Stute and Wang (1994) considered the problem of estimating the integralS(r)=∫rdF, based on a possibly censored sample from a distribution F, where r is an F-integrable function. They proposed a Kaplan-Meier integralSn^(r) to approximate S(r) and derived an explict formula for thedelete-1 jackknife estimate of Sn^(r).In a small simulation study for themean lifetimes of exponential variables,they claimed that jackknifing ledto a reduction of bias.In this note, it is pointed out that Sn^(r) is basedon a defective distribution, and therefore Sn^(r) and the delete-1jackknife estimate of Sn^(r) are both badly biased. According to Efron (1981),we propose a modified estimator Sn~(r) and derive explicit formulas for thedelete-1 and delete-2 jackknife estimates of Sn~(r).Simulation resultsdemonstrate that the modified estimates are much less biased than thosefrom Stute and Wang (1994).KEY WORDS: jackknife; Kaplan-Meier estimators;censored data.-1 -aThe jackknife estimates of a Kaplan-Meier integral-zeng- 0-a - 1-ajackknife-aKaplan-Meier estimators-acensored data
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