A combinatoric approach to the kaplan-meier estimator

The paper considers the Kaplan-Meier estimator FKMn from a combinatoric viewpoint. Under the assumption that the estimated distribution F and the censoring distribution G are continuous, the combinatoric results are used to show that ∫|θ(z)|dFKMn(z) has expectation not larger than ∫|θ(z)|dF(z) for any sample size n. This result is then coupled with Chebychev's inequality to demonstrate the weak convergence of the former integral to the latter if the latter is finite, if F and G are strictly less than 1 on R and if θ is continuous.