Multiply robust estimation in nonparametric regression with missing data

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.