缺失数据下线性模型的半参数估计  

Semiparametric Estimation for Linear Models with Missing Data

作　　者：赵洋[1,2] 薛留根[1] 胡玉琴[1,3] 

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]南昌大学理学院,江西南昌330031 [3]浙江财经大学数据科学学院,浙江杭州310018

出　　处：《数学的实践与认识》2016年第16期191-197,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11571025;重点项目:11331011);北京市自然科学基金(1142003;L140003)

摘　　要：通过比较参数方法和非参数方法对选择概率建模的优缺点,基于充分降维的思想提出了一种利用单指标模型对选择概率建模的半参数方法.基于逆概率加权方法和半参数方法,研究了缺失数据下线性模型的统计推断问题.建立的逆概率加权估计方程可以处理不同的数据缺失情形,给出了线性模型中兴趣参数的估计,并证明了它的渐近正态性.最后通过模拟研究说明提出的方法具有较好的有限样本性质.Comparing the advantages and disadvantages of the selection probability modeling between the parametric method and the nonparametric method, we propose a semiparametric method based on the idea of sufficient dimension reduction, to model the selection probability by a single-index model. This paper examine the problem of estimation for the interesting parameters in a linear model, when some observed variables are missing at random. To handle different missing data cases, we develop the inverse probability weighted estimating equations by the proposed semiparametric method, and prove our method yield estimators that achieve the asymptotic property of normality. Simulation studies are conducted to examine the finite sample performance of the proposed procedure.

关 键 词：单指标模型 随机缺失 选择概率 逆概率加权 线性模型. 

分 类 号：O212.1[理学—概率论与数理统计]