Primary Submission Category: Machine Learning and Causal Inference
Higher-order estimators of time-varying effects in anisotropic smoothness models
Authors: Matteo Bonvini, Edward H. Kennedy, Luke J. Keele,
Presenting Author: Matteo Bonvini*
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 yielded 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. In this work, we aim to extend the application of HOIF theory to causal parameters defined by a time-varying treatment. As a leading example, we consider the two-time point case g-formula functional in an anisotropic smoothness model where the nuisance functions can depend more smoothly on certain covariates. We also consider even more structured models, such as additive ones. In each setting, we design a higher-order estimator and calculate its bias and variance, and for some of them, we show that the convergence rates established are minimax optimal. We complement our theoretical findings with simulations and data analysis.