A Unifying Approach for Doubly-Robust L1-Regularized Estimation of Causal Contrasts

• Activity Number: 103 - Semiparametric Inference with High-Dimensional and Complex Data
• Type: Invited
• Date/Time: Monday, August 3, 2020 : 1:00 PM to 2:50 PM
• Sponsor: ENAR
• Author(s): Ezequiel Smucler* and James Robins and Andrea Rotnitzky
• Companies: Universidad Torcuato Di Tella and Harvard T.H Chan School of Public Health and Universidad Torcuato Di Tella
• Keywords: double robustness; causal inference; lasso

Abstract

We study a class of parameters with the so-called ‘mixed bias property’, which contains many parameters of interest in causal inference, such as the ATE and the ATT. For parameters with this property, the bias of the one-step estimator is equal to the mean of the product of the estimation errors of two nuisance functions. In non-parametric models, parameters with the mixed bias property admit so-called rate doubly robust estimators, i.e. estimators that are consistent and asymtotically normal when one succeeds in estimating both nuisance functions at sufficiently fast rates, with the possibility of trading off slower rates of convergence for the estimator of one of the nuisance functions with faster rates for the estimator of the other nuisance. We characterize the form of parameters with the mixed bias property and of their influence functions. Finally, we propose a general estimation strategy based on l1-regularized estimators of the nuisance functions that yields doubly-robust estimators for any parameter with the mixed bias property.