摘要
本文在生存时间和删失时间均为宽相依数据下,建立了生存函数的Kaplan-Meier估计和风险率估计的强逼近和强表示,获得的强逼近和强表示误差项的收敛速度达到O(n^(-1/2)log^(1/2)n).所得结果推广了负相协和负超可加相依数据情形下的相关结果.
Consider the survival function and hazard rate estimators by the Kaplan-Meier method based on censored data, where the survival and censoring times come from the widely orthant dependent date, respectively. Under some more mild conditions, the uniform strong approximation rates and strong representation for the survival function and hazard rate are investigated, and their uniform strong approximation rates and remainders of strong representation also are obtained with the order O(n-1/2 log1/2n) a.s. Our results established generalize the corresponding ones of negatively associated and negatively superadditive dependent data in the related literatures.
作者
李永明
周勇
LI Yongming;ZHOU Yong(School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China 200433, China;School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001, China;Faculty of Economics and management, East China Normal University, Shanghai 200062, China)
出处
《应用数学学报》
CSCD
北大核心
2019年第1期71-84,共14页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金项目(11461057
11561010)
国家自然科学基金重点项目(71331006)
国家自然科学重大研究计划重点项目(91546202)资助
关键词
宽相依
Kaplan-Meier估计
强逼近和强表示
生存函数
风险率估计
widely orthant dependent
Kaplan-Meier estimator
strong approximation and representation
survival function
hazard rate estimator
