SOME INEQUALITIES ABOUT THE KAPLAN-MEIER ESTIMATOR

• 成果类型: Article
• 署名作者: YANG, S
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348537
• 发表日期: 1992
• 页码: 535-544
• 关键词: survival

摘要

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.