A0576
Title: Higher-order estimators of time-varying effects in anisotropic smoothness models
Authors: Edward Kennedy - Carnegie Mellon University (United States)
Luke Keele - University of Pennsylvania (United States)
Matteo Bonvini - Rutgers University (United States) [presenting]
Abstract: The general theory of higher-order influence functions (HOIF) has been successfully applied to several pathwise differentiable parameters arising in causal inference, such as the expected conditional covariance and the treatment-specific mean. Such theory has been shown to yield minimax optimal estimators in certain nonparametric models, e.g., those indexed by smooth nuisance parameters. More recently, minimax optimal, higher-order estimators have been derived for some non-pathwise differentiable causal parameters, an example of which is the conditional average treatment effect. The aim is to extend the application of HOIF theory to causal parameters defined by a time-varying treatment. As a leading example, the two-time point case g-formula is considered functional in an anisotropic smoothness model where the nuisance functions are allowed to depend more smoothly on certain covariates. More structured models are also considered, such as additive ones. In each setting, a higher-order estimator is designed and its bias and variance are calculated, and for some of them, it is shown that the convergence rates established are minimax optimal. The findings are complemented with a simulation study.
