Multiply Robust Estimator Circumvents Hyperparameter Tuning of Neural Network Models in Causal Inference

Estimation of the Average Treatment Effect (ATE) is often carried out in 2 steps, wherein the first step, the treatment and outcome are modeled, and in the second step the predictions are inserted into the ATE estimator. In the first steps, numerous models can be fit to the treatment and outcome, including using machine learning algorithms. However, it is a difficult task to choose among the hyperparameter sets which will result in the best causal effect estimation and inference. Multiply Robust (MR) estimator allows us to leverage all the first-step models in a single estimator. We show that MR estimator is $n^r$ consistent if one of the first-step treatment or outcome models is $n^r$ consistent. We also show that MR is the solution to a broad class of estimating equations, and is asymptotically normal if one of the treatment models is $\sqrt{n}$-consistent. The standard error of MR is also calculated which does not require a knowledge of the true models in the first step. Our simulations study supports the theoretical findings.