Missing data is frequently encountered in many areas of statistics. Propensity score weighting is a popular method for handling missing data. The propensity score method employs a response propensity model, but correct specification of the statistical model can be challenging in the presence of missing data. Doubly robust estimation is attractive, as the consistency of the estimator is guaranteed when either the outcome regression model or the propensity score model is correctly specified. In this paper, we first employ information projection to develop an efficient and doubly robust estimator under indirect model calibration constraints. The resulting propensity score estimator can be equivalently expressed as a doubly robust regression imputation estimator by imposing the internal bias calibration condition in estimating the regression parameters. In addition, we generalize the information projection to allow for outlier-robust estimation. Some asymptotic properties are presented. The simulation study confirms that the proposed method allows robust inference against not only the violation of various model assumptions, but also outliers. A real-life application is presented using data from the Conservation Effects Assessment Project.

翻译：缺失数据在统计学的许多领域经常出现。倾向性得分加权是处理缺失数据的常用方法。倾向性得分方法采用响应倾向性模型，但在存在缺失数据的情况下，正确设定统计模型可能颇具挑战性。双重稳健估计具有吸引力，因为当结果回归模型或倾向性得分模型之一被正确指定时，估计量的一致性得到保证。本文首先利用信息投影，在间接模型校正约束下发展一种高效且双重稳健的估计量。通过在回归参数估计中施加内部偏差校正条件，得到的倾向性得分估计量可等价地表达为双重稳健回归插补估计量。此外，我们将信息投影推广到允许鲁棒于异常值的估计。给出了部分渐近性质。模拟研究证实，所提方法不仅在违反各种模型假设时具有鲁棒性，而且对异常值也保持稳健。利用保护效果评估项目的数据给出了实际应用案例。