ESTIMATING A DISTRIBUTION FUNCTION WITH TRUNCATED AND CENSORED-DATA

• 成果类型: Article
• 署名作者: LAI, TL; YING, ZL
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176347991
• 发表日期: 1991
• 页码: 417-442
• 关键词: product-limit estimator; large sample

摘要

A minor modification of the product-limit estimator is proposed for estimating a distribution function (not necessarily continuous) when the data are subject to either truncation or censoring, or to both, by independent but not necessarily identically distributed truncation-censoring variables. Making use of martingale integral representations and empirical process theory, uniform strong consistency of the estimator is established and weak convergence results are proved for the entire observable range of the function. Numerical results are also given to illustrate the usefulness of the modification, particularly in the context of truncated data.