A further study of the multiply robust estimator in missing data analysis

• An easy-to-compute multiply robust estimator for missing data analysis.
• Sample bounded estimator.
• Insensitive to extreme values of the estimated missingness probability.

In estimating the population mean of a response variable that is missing at random, the estimator proposed by Han and Wang (2013) possesses the multiple robustness property, in the sense that it is consistent if any one of the multiple models for both the missingness probability and the conditional expectation of the response variable given the covariates is correctly specified. This estimator is a significant improvement over the existing doubly robust estimators in the literature. However, the calculation of this estimator is difficult, as it requires solving equations that may have multiple roots, and only when the appropriate root is used is the final estimator multiply robust. In this paper, we propose a new way to define and calculate this estimator. The appropriate root is singled out through a convex minimization, which guarantees the uniqueness. The new estimator possesses other desirable properties in addition to multiple robustness. In particular, it always falls into the parameter space, and is insensitive to extreme values of the estimated missingness probability.