We study the problem of estimating a functional or a parameter in the context where outcome is subject to nonignorable missingness. We completely avoid modeling the regression relation, while allowing the propensity to be modeled by a semiparametric logistic relation where the dependence on covariates is unspecified. We discover a surprising phenomenon in that the estimation of the parameter in the propensity model as well as the functional estimation can be carried out without assessing the missingness dependence on covariates. This allows us to propose a general class of estimators for both model parameter estimation and functional estimation, including estimating the outcome mean. The robustness of the estimators are nonstandard and are established rigorously through theoretical derivations, and are supported by simulations and a data application.

翻译：我们研究在结果不可忽略的情况下估计功能或参数的问题。 我们完全避免模拟回归关系,同时允许在依赖共差的半对数后勤关系中以对共差的依赖性为模型进行模拟。 我们发现一个令人惊讶的现象,即在不评估对共差的依赖性的情况下,可以对偏差模型中的参数和功能估计进行估计,而不必评估对共差的缺失性依赖性。这使我们能够为模型参数估计和功能估计,包括估计结果平均值,提出一个一般的估测者类别。估计者的稳健性是非标准性的,通过理论推论严格确立,并得到模拟和数据应用的支持。