THE STRONG LAW UNDER RANDOM CENSORSHIP

• 成果类型: Article
• 署名作者: STUTE, W; WANG, JL
• 署名单位: University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349273
• 发表日期: 1993
• 页码: 1591-1607
• 关键词: product-limit estimator; Kaplan-Meier estimator; uniform consistency

摘要

Let X1, X2, ... be a sequence of i.i.d. random variables with d.f. F. We Observe Z(i) = min(X(i), Y(i)) and delta(i) = 1(Xi less-than-or-equal-to Yi), where Y1, Y2, ... is a sequence of i.i.d. censoring random variables. Denote by F(n) the Kaplan-Meier estimator of F. We show that for any F-integrable function phi, integral phi dF(n) converges almost surely and in the mean. The result may be applied to yield consistency of many estimators under random censorship.