协变量随机删失时部分线性模型的估计  

Estimation of Partially Linear Model with Randomly Right-censored Covariate

作　　者：鲁小凡 孙志华 王晴晴 LU Xiao-fan;SUN Zhi-hua;WANG Qing-qing(School of Economics and Management,University of Chinese Academy of Sciences,Beijing 100049,China;School of Mathematic Sciences,University of Chinese Academy of Sciences,Beijing 100191,China)

机构地区：[1]中国科学院大学经济与管理学院,北京100191 [2]中国科学院大学数学科学学院,北京100049

出　　处：《数理统计与管理》2022年第2期279-293,共15页Journal of Applied Statistics and Management

基　　金：北京市国家自然科学基金(Z200001,1202001);国家自然科学基金(12071457,11971045);中央高校基本科研业务费专项资金和中国科学院大数据挖掘与知识管理重点实验室开放课题资助.

摘　　要：在很多研究领域,数据经常出现右删失的情况.响应变量出现右删失时的统计估计问题吸引了很多关注.然而协变量出现右删失的情况并未受到应有的关注.本文对协变量出现删失时的部分线性模型的估计问题进行研究.我们采用逆概率加权方法对协变量的删失进行处理,构建了回归系数和非参数函数的估计,证明了估计的渐近性质,数值模拟和实例分析结果表明所提方法表现很好。Statistical analyses in research fields such as medicine often involves the right censoring of covariates.Although studies on statistical estimation with right censored response variable has attracted a lot of attention,the right censorship in covariates has not received the attention they deserve.This paper studies the estimation of a partially linear model when covariates are randomly rightly-censored.We adjured the censored covariates,constructed regression estimates and nonparametric function estimates,and proved the asymptotic properties of the estimates.Numerical simulation studies and real data analyses show that the proposed method performs well.

关 键 词：随机右删失 部分线性模型 逆概率加权 渐近正态性 

分 类 号：O212[理学—概率论与数理统计] O213.2[理学—数学]