In this paper we consider the product-limit estimator of the survival distribution function in the context of independent but nonidentically distributed censoring times. An upper bound on the mean square increment of the stopped Kaplan-Meier process is obtained. Also, a representation is given for the ratio of the survival distribution function to the product-limit estimator as the product of a bounded process and a martingale. From this representation bounds on the mean square of the ratio and on the tail probability of the sup norm of the ratio are derived.
"Some Inequalities About the Kaplan-Meier Estimator." Ann. Statist. 20 (1) 535 - 544, March, 1992. https://doi.org/10.1214/aos/1176348537