Efficient Estimation under Multiple Missing Patterns via Balancing Weights

As one of the most commonly seen data challenges, missing data, in particular, multiple, non-monotone missing patterns, complicates estimation and inference due to the fact that missingness mechanisms are often not missing at random, and conventional methods cannot be applied. Pattern graphs have recently been proposed as a tool to systematically relate various observed patterns in the sample. We extend its scope to the estimation of parameters defined by moment equations, including common regression models, via solving weighted estimating equations with weights constructed using a sequential balancing approach. These novel weights are carefully crafted to address the instability issue of the straightforward approach based on local balancing. We derive the efficiency bound for the model parameters and show that our proposed method, albeit relatively simple, is asymptotically efficient. Simulation results demonstrate the superior performance of the proposed method, and real-data applications illustrate how the results are robust to the choice of identification assumptions.