缺失数据下线性模型的半参数估计

Semiparametric Estimation for Linear Models with Missing Data

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.