A0898
Title: Dynamic treatment effects: High-dimensional inference under model misspecification
Authors: Yuqian Zhang - Renmin University of China (China) [presenting]
Jelena Bradic - University of California San Diego (United States)
Weijie Ji - University of California San Diego (United States)
Abstract: The estimation and inference of average treatment effects in dynamic settings are considered, where covariates and treatments are longitudinal. We focus on high-dimensional cases when the sample size $N$ is potentially much smaller than the covariate vectors dimension $d$. The marginal structural mean models are considered. We identify a new, broad doubly (multiply) robust estimator, which we name a ``sequential model doubly robust estimator''. We achieve root-$N$ inference even when model misspecification occurs. For that purpose, new loss functions and new nuisance parameters are introduced, named "moment targeted", aimed to reduce the bias of model misspecification. New loss functions resolve a long-standing open problem of dynamic double robustness. We identify the weakest conditions up to date that match naive intuition. Multiple time model double robustness is achieved whenever each time exposure is model doubly-robust itself. This significantly extends the literature even in low-dimensions, where the doubly robust property requires a number of complex conditions to hold.
