On the rate of uniform convergence of the product-limit estimator: Strong and weak laws

• 成果类型: Article
• 署名作者: Chen, K; Lo, SH
• 署名单位: Hong Kong University of Science & Technology; Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1050-1087
• 关键词: random censorship; large sample; regression; INTEGRALS

摘要

By approximating the classical product-limit estimator of a distribution function with an average of iid random variables, we derive sufficient and necessary conditions for the rate of(both strong and weak) uniform convergence of the product-limit estimator over the whole line. These findings somehow fill a longstanding gap in the asymptotic theory of survival analysis. The result suggests a natural way of estimating the rate of convergence. We also prove a related conjecture raised by Gill and discuss its application to the construction of a confidence interval for a survival function near the endpoint.