Robust semiparametric estimators: missing data and causal inference

Semiparametric inference with missing outcome data (including causal inference) is based on partially specified models which are not of direct interest (e.g., model for missingness/treatment assignment mechanism). Different class of estimators exist, which are more or less robust to misspecification of these models. Another type of threat to the validity of the inference occur in situations where some observations are contaminated (generated by some nuisance distribution). Classical semiparametric inference is not robust to such contamination, and a single observation may have an arbitrary large effect on bias as measured by the influence function. We introduce inverse probability weighted, double robust and outcome regression estimators of location and scale parameters, which are robust to contamination in the sense that their influence function is bounded. We give asymptotic properties and study finite sample behaviour. Our simulated experiments show that contamination can be more serious a threat to the quality of inference than model misspecification. An interesting aspect of our results is that the auxiliary outcome model used to adjust for ignorable missingness (confounding) is also useful to protect against contamination. We also illustrate through a case study how both adjustment to ignorable missingness and protection against contamination are achieved through weighting schemes, which can be contrasted to gain further insights.