基于右删失宽相依数据的Kaplan-Meier估计和风险率估计的渐近性质  

Asymptotic Properties of the Kaplan-Meier Estimator and Hazard Rate Estimator for Right Censored and Widely Orthant Dependent Data

作　　者：李永明 周勇[3] 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)

机构地区：[1]上海财经大学统计与管理学院,上海200433 [2]上饶师范学院数学与计算机科学学院,上饶334001 [3]华东师范大学经济与管理学部,上海200062

出　　处：《应用数学学报》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

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.

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 

分 类 号：O212.7[理学—概率论与数理统计]