基于判断事后分层抽样下删失数据的保序估计  

The Isotonized Estimation in Judgment Poststratified Sample with Censoring

作　　者：李涛 韩子璇 LI TAO;HAN ZIXUAN(School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai 200433,China)

机构地区：[1]上海财经大学统计与管理学院,上海200433

出　　处：《应用数学学报》2022年第2期145-167,共23页Acta Mathematicae Applicatae Sinica

基　　金：教育部社科基金(21YJA910001)资助项目。

摘　　要：本文讨论了判断事后分层抽样下生存函数的Kaplan-Meier估计及其大样本性质.此外,基于判断事后分层抽样下各层序的信息,对样本进行保序回归,根据样本中是否存在空层的情况提出了不同的保序Kaplan-Meier估计,并讨论各估计的性质.本文通过模拟对判断事后分层样本下的各种Kaplan-Meier估计以及简单随机样本下的Kaplan-Meier估计进行比较,结果显示判断事后分层抽样比简单随机抽样更有效,并且保序估计方法可以提升估计的效率.Based on the judgment poststratified sample with censoring,we discuss the Kaplan-Meier estimator for survival function and its asymptotic property.With the rank information of judgment poststratified sample,we also propose several isotonized KaplanMeier estimators and their asymptotic properties.Moreover,we conduct the simulation studies to compare the performance of all estimators based on judgment poststratified sample with the Kaplan-Meier estimator based on simple random sample and show that the estimations based on judgment poststratified sample is more efficient than the estimator based on simple random sample,and the isotonic regression method can improve the efficiency of the estimation.Meanwhile,based on the several Kaplan-Meier estimators,we construct the corresponding mean estimators and compare their performance under various settings,the results present the similar patterns of estimators of survival functions.Moreover,we study the impact of imperfect ranking on these estimators by setting different relative coefficients between variable of interests and covariate.The estimators under imperfect ranking show similar performance with that under perfect ranking,and the increase of relative coefficient can improve the relative efficiency of estimators.A real data analysis is also conducted to show the efficiency of the proposed estimators.

关 键 词：判断事后分层抽样 Kaplan-Meier估计 保序回归 生存函数 

分 类 号：O212.2[理学—概率论与数理统计]