Some Inequalities About the Kaplan-Meier Estimator
The Annals of Statistics · 1992 · Volume 20 · Issue 1
Abstract
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.
Keywords
62E20; 62G99; 62M99; Gronwall's inequality; martingale; product-limit estimator; Volterra integral equation;
Enable JavaScript for citation tools and additional paper interactions.