Edward Kennedy: Optimal doubly robust estimation of heterogeneous causal effects

"Optimal doubly robust estimation of heterogeneous causal effects"
Edward Kennedy: Carnegie Mellon University
Discussant: James Robins, Harvard University
Abstract: Heterogeneous effect estimation has become a major enterprise in causal inference, with ramifications across medicine and social science, e.g., improving understanding of variation, as well as informing policy and optimizing treatment decisions. Many methods for estimating the conditional average treatment effect (CATE) have been proposed in recent years; however, there are important gaps in the literature, particularly on the theory side, vis-a-vis understanding if and when such methods can be optimal. These gaps are especially pronounced in settings where the CATE is more structured and less complex than the rest of the data-generating process. We contribute in several main ways. First, we study a two-stage doubly robust CATE estimator, similar to that proposed by van der Laan (2013) and used by others since. We give a generic model-free error bound, which, despite its generality, yields sharper results than those in the current literature. Second, we illustrate the results in nonparametric models with smoothness or sparsity, and give sufficient conditions for oracle efficiency, depending on nuisance structure. Underlying our error bound is a general oracle inequality for regression with estimated or imputed outcomes, which is of independent interest; this is the third main contribution. The fourth contribution is aimed at understanding the fundamental statistical limits of CATE estimation. To that end, we propose and study a local polynomial adaptation of the R-Learner and double-residual regression (Nie & Wager 2017, Robinson 1998). We show that this estimator is oracle efficient under weaker conditions than the first estimator, when using a specialized form of sample splitting and careful choices of tuning parameters. These conditions are the weakest currently found in the literature, and we conjecture that they are minimal in a minimax sense. We go on to give error bounds in the challenging regime where oracle rates cannot be achieved. We illustrate our results and study finite-sample properties with simulations.
April 28, 2020