协变量随机右删失时变系数模型的估计  

Estimation of Varying Coeficient Model with Randomly Right-Censored Covariate

作　　者：柴旺 尹俊平[2,3,4] 孙志华 CHAI Wang;YIN Junping;SUN Zhihua(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing,100049,China;Institute of Applied Physics and Computational Mathematics,Beijing,100094,China;National Key Laboratory of Computational Physics,Beijing,100088,China;Shanghai Zhangjiang Institute of Mathematics,Shanghai,201203,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049 [2]北京应用物理与计算数学研究所,北京100094 [3]计算物理全国重点实验室,北京100088 [4]上海张江数学研究院,上海201203

出　　处：《应用概率统计》2024年第5期800-818,共19页Chinese Journal of Applied Probability and Statistics

基　　金：北京市自然科学基金重点项目(批准号:Z200001);国家自然科学基金项目(12071457,12271504);国家自然科学基金重点项目(批准号:12031016);国家自然科学基金重大项目(批准号:12292980,12292984)资助;国家重点研发计划(批准号:2023YFA1009000,2023YFA1009004,2020YFA0712203,2020YFA0712201)。

摘　　要：数据经常因为个体失访,退出实验或者研究结束而出现右删失的现象.右删失数据的研究吸引了很多研究者的兴趣.文献中大部分研究集中在响应变量出现右删失的情况.回归模型中的协变量也可能出现右删失,但相关的研究并不多.本文研究协变量随机右删失时变系数模型的估计问题.我们利用逆概率加权方法直接对目标函数进行调整,而不是调整被删失的协变量,来处理数据的删失.所得估计的渐近性质得到严格证明.通过数值模拟和实例分析,可以看到本文所提方法具有很好的有限样本性质.Data is often right-censored due to loss of follow-up,drop-out from experiments or end of clinical trials.The treatment of right-censored data has attracted the interest of many researchers.Most existing studies focus on the cases where the response variable is censored.Predictors in the regression model may also suffer from right-censoring.However,there are only sporadic works on the treatment of censored covariates.In this paper,the estimation of a varying coefficient model with randomly right-censored covariates is investigated.To deal with the right-censoring,we adjust the objective function directly through an inverse probability weighting,instead of adjusting the right-censored predictor.Es-timation of the regression coefficient is proposed.The asymptotic properties of the proposed estimator are rigorously investigated.Numerical simulations and real-data analyses demonstrate that the proposed method has good finite sample properties.

关 键 词：变系数模型 局部线性估计 随机右删失协变量 渐近性质 

分 类 号：O212.7[理学—概率论与数理统计]