Abstract We address the characterization of problems in which a consistent estimator exists in a union of two models, also termed as a doubly robust estimator. Such estimators are important in missing information, including causal inference problems. Existing characterizations, based on the semiparametric theory of projections, have seen sufficient progress, but can still leave one’s understanding less than satisfied as to when and especially why such estimation works. We explore here a different, explanatory characterization – an exegesis based on logical operators. We show that double robustness exists if and only if we can produce consistent estimators for each contributing model based on an “AND” estimator, i. e., an estimator whose consistency generally needs both models to be correct. We show how this characterization explains double robustness through falsifiability.

中文翻译：

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通过逻辑运算符的双重鲁棒性的可证伪性表征

摘要 我们解决了在两个模型的联合中存在一致估计量的问题的表征，也称为双重稳健估计量。这种估计量在缺失信息中很重要，包括因果推理问题。基于投影的半参数理论的现有表征已经取得了足够的进展，但对于何时以及尤其是为什么这种估计有效，人们的理解仍然不尽如人意。我们在这里探索一种不同的解释性特征——一种基于逻辑运算符的释经。我们表明，当且仅当我们可以基于“AND”估计量为每个贡献模型生成一致的估计量时，才存在双重稳健性，即。例如，一个估计器的一致性通常需要两个模型都是正确的。