Nonignorable Missing Data, Single Index Propensity Score and Profile Synthetic Distribution Function
针对缺失非随机的数据问题，提出一种基于单指标模型的倾向得分估计方法，通过轮廓合成分布函数构造伪似然，得到渐近正态估计，模拟显示优于现有方法。
In missing data problems, missing not at random is difficult to handle since the response probability or propensity score is confounded with the outcome data model in the likelihood. Existing works often assume the propensity score is known up to a finite dimensional parameter. We relax this assumption and consider an unspecified single index model for the propensity score. A pseudo-likelihood based on the complete data is constructed by profiling out a synthetic distribution function that involves the unknown propensity score. The pseudo-likelihood gives asymptotically normal estimates. Simulations show the method compares favorably with existing methods.