Imputation and the inverse probability weighting are two commonly used approaches in missing data analysis. Parametric versions of them are not robust due to model misspecification of some unknown functions. Nonparametric ones are robust but are impractical when the number of covariates is large due to the problem of “curse of dimension”. A beyond multiple robust method is proposed in this paper. This method balances the parametric and nonparametric methods by using some model information contained in the outcome regression function and the selection probability function, and hence alleviates the model misspecification problem and “curse of dimension” problem simultaneously. To illustrate the proposed method, we focus on the estimating problem of response mean in the presence of missing responses. A beyond multiple robust estimator of the response mean is defined, which is proved to be consistent and asymptotically normal as long as one of the true models for the outcome regression or selection probability functions can be some function of its assumed models, without the requirement that one of the true models is correctly specified. Also, it is shown that the asymptotic variance of the proposed estimator is equal to the semiparametric efficiency bound established by Hahn (1998, Econometrica, pp 315–331) when both the selection probability function and the outcome regression function are the functions of their assumed models, respectively. The finite sample properties of the proposed estimator are evaluated by simulation studies and the proposed method is illustrated by a real data analysis.

中文翻译：

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一种针对缺失响应问题的超越多重稳健方法

插补和逆概率​​加权是缺失数据分析中两种常用的方法。由于某些未知函数的模型指定错误，它们的参数版本并不健壮。非参数方法是稳健的，但由于“维度诅咒”的问题，当协变量的数量很大时不切实际。本文提出了一种超越多重鲁棒性的方法。该方法通过使用结果回归函数和选择概率函数中包含的一些模型信息来平衡参数和非参数方法，从而同时缓解模型错误指定问题和“维度诅咒”问题。为了说明所提出的方法，我们专注于在存在缺失响应的情况下估计响应均值的问题。定义了响应均值的超多个稳健估计量，只要结果回归或选择概率函数的真实模型之一可以是其假设模型的某个函数，则证明它是一致且渐近正态的，而不要求正确指定了真实模型之一。Also, it is shown that the asymptotic variance of the proposed estimator is equal to the semiparametric efficiency bound established by Hahn (1998, Econometrica, pp 315–331) when both the selection probability function and the outcome regression function are the functions of their assumed模型，分别。所提出的估计器的有限样本特性通过模拟研究进行评估，所提出的方法通过实际数据分析进行说明。只要结果回归或选择概率函数的真实模型之一可以是其假设模型的某些函数，则证明是一致且渐近正态的，而无需正确指定其中一个真实模型。Also, it is shown that the asymptotic variance of the proposed estimator is equal to the semiparametric efficiency bound established by Hahn (1998, Econometrica, pp 315–331) when both the selection probability function and the outcome regression function are the functions of their assumed模型，分别。所提出的估计器的有限样本特性通过模拟研究进行评估，所提出的方法通过实际数据分析进行说明。只要结果回归或选择概率函数的真实模型之一可以是其假设模型的某个函数，而无需正确指定其中一个真实模型，则证明它是一致且渐近正态的。Also, it is shown that the asymptotic variance of the proposed estimator is equal to the semiparametric efficiency bound established by Hahn (1998, Econometrica, pp 315–331) when both the selection probability function and the outcome regression function are the functions of their assumed模型，分别。所提出的估计器的有限样本特性通过模拟研究进行评估，所提出的方法通过实际数据分析进行说明。