For estimating the population mean of a response variable subject to ignorable missingness, a new class of methods, called multiply robust procedures, has been proposed. The advantage of multiply robust procedures over the traditional doubly robust methods is that they permit the use of multiple candidate models for both the propensity score and the outcome regression, and they are consistent if any one of the multiple models is correctly specified, a property termed multiple robustness. This paper shows that, somewhat surprisingly, multiply robust estimators are special cases of doubly robust estimators, where the final propensity score and outcome regression models are certain combinations of the candidate models. To further improve model specifications in the doubly robust estimators, we adapt a model mixing procedure as an alternative method for combining multiple candidate models. We show that multiple robustness and asymptotic normality can also be achieved by our mixing-based doubly robust estimator. Moreover, our estimator and its theoretical properties are not confined to parametric models. Numerical examples demonstrate that the proposed estimator is comparable to and can even outperform existing multiply robust estimators.

中文翻译：

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揭开一类乘法稳健估计量的神秘面纱

为了估计易失性缺失的响应变量的总体平均值，提出了一种新的方法，称为乘稳健程序。与传统的双稳健方法相比，健壮稳健程序的优势在于，它们允许对倾向得分和结果回归使用多个候选模型，并且如果正确指定了多个模型中的任何一个，则它们是一致的，该属性称为多重鲁棒性。本文显示出令人惊讶的是，乘稳健估计是双稳健估计的特殊情况，其中最终倾向得分和结果回归模型是候选模型的某些组合。为了进一步提高双稳健估计器中的模型规格，我们采用模型混合程序作为组合多个候选模型的替代方法。我们表明，通过基于混合的双重鲁棒估计量，也可以实现多重鲁棒性和渐近正态性。此外，我们的估计量及其理论性质不限于参数模型。数值算例表明，所提出的估计量与现有的乘稳健估计量相当，甚至可以胜过现有的估计。