# Robust semiparametric inference with missing data

## TL;DR

This paper develops robust semiparametric estimators for missing data that are resistant to contamination, outperforming traditional methods especially under data contamination scenarios.

## Contribution

It introduces inverse probability weighted, double robust, and outcome regression estimators with bounded influence functions, enhancing robustness against data contamination.

## Key findings

- Contamination poses a greater threat to inference than model misspecification.
- Auxiliary outcome models can protect against contamination while adjusting for missing data.
- Simulations demonstrate improved robustness of proposed estimators under contamination.

## Abstract

Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is exacerbated when inverse probability weighting methods are used, which may overweight contaminated observations. 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 by some of the estimators, 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.