Nonparametric regression has received considerable attention in biomedical research because it allows for data-driven dependence of the response variable on covariates. In the presence of missing data, doubly robust estimators have been proposed for nonparametric regression, which allow one model for the missingness mechanism and one model for the outcome regression. We propose multiply robust kernel estimating equations (MRKEEs) for nonparametric regression that can accommodate multiple working models for either the missingness mechanism or the outcome regression, or both. The resulting estimator is consistent if any one of those models is correctly specified. When including correctly specified models for both the missingness mechanism and the outcome regression, the proposed estimator achieves the optimal efficiency within the class of augmented inverse propensity weighted (AIPW) kernel estimators. We conduct simulation studies to evaluate the finite sample performance of the proposed method and further demonstrate it through a real-data example.

中文翻译：

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用缺失数据乘以非参数回归中的稳健估计

非参数回归在生物医学研究中受到了相当大的关注，因为它允许响应变量对协变量的数据驱动依赖性。在存在缺失数据的情况下，已经为非参数回归提出了双稳健估计器，这允许使用一种模型用于缺失机制和一种模型用于结果回归。我们为非参数回归提出了多重稳健核估计方程 (MRKEE)，它可以适应缺失机制或结果回归或两者的多种工作模型。如果正确指定了这些模型中的任何一个，则生成的估计量是一致的。当为缺失机制和结果回归包含正确指定的模型时，建议的估计器在增强逆倾向加权 (AIPW) 核估计器类中实现了最佳效率。我们进行模拟研究以评估所提出方法的有限样本性能，并通过真实数据示例进一步证明它。