On varieties of doubly robust estimators under missingness not at random with a shadow variable
本文针对结果变量缺失非随机但有完全观测的影子变量（与结果相关但与缺失机制独立）的情形，提出了两种新的双重稳健估计量，并给出了模型正确性的拟合优度检验方法。
Suppose we are interested in the mean of an outcome variable missing not at random. Suppose however that one has available a fully observed shadow variable, which is associated with the outcome but independent of the missingness process conditional on covariates and the possibly unobserved outcome. Such a variable may be a proxy or a mismeasured version of the outcome and is available for all individuals. We have previously established necessary and sufficient conditions for identification of the full data law in such a setting, and have described semiparametric estimators including a doubly robust estimator of the outcome mean. Here, we propose two alternative estimators, which may be viewed as extensions of analogous methods under missingness at random, but enjoy different properties. We assess the correctness of the required working models via straightforward goodness-of-fit tests.