A unifying approach for doubly-robust $\ell_1$ regularized estimation of causal contrasts

By Ezequiel Smucler, Andrea Rotnitzky, James M. Robins. 2019

87 citations recorded by the source corpus.

We consider inference about a scalar parameter under a non-parametric model based on a one-step estimator computed as a plug in estimator plus the empirical mean of an estimator of the parameter's influence function. We focus on a class of parameters that have influence function which depends on two infinite dimensional nuisance functions and such that the bias of the one-step estimator of the parameter of interest is the expectation of the product of the estimation errors of the two nuisance functions. Our class includes many important treatment effect contrasts of interest in causal inference and econometrics, such as ATE, ATT, an integrated causal contrast with a continuous treatment, and the mean of an outcome missing not at random. We propose estimators of the target parameter that entertain approximately sparse regression models for the nuisance functions allowing for the number of potential confounders to be even larger than the sample size. By employing sample splitting, cross-fitting and $\ell_1$-regularized regression estimators of the nuisance functions based on objective functions whose directional derivatives agree with those of the parameter's influence function, we obtain estimators of the target parameter with two desirable robustness properties: (1) they are rate doubly-robust in that they are root-n consistent and asymptotically normal when both nuisance functions follow approximately sparse models, even if one function has a very non-sparse regression coefficient, so long as the other has a sufficiently sparse regression coefficient, and (2) they are model doubly-robust in that they are root-n consistent and asymptotically normal even if one of the nuisance functions does not follow an approximately sparse model so long as the other nuisance function follows an approximately sparse model with a sufficiently sparse regression coefficient.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, background): “This kind of double robustness is sometimes called model double robustness (Smucler et al., 2019) because the rates needed essentially correspond to parametric estimation and therefore the conditions refer to whether these parametric models are well-speciﬁed.”
Characterization of parameters with a mixed bias property (2019, background): “In a separate article Smucler et al. (2019) we report a unified strategy for the construction of onestep, sample-splitted and cross-fitted estimators of parameters that have the mixed bias property with the nuisance functions estimated via ℓ1 regularization.”
Efficiently Breaking the Curse of Horizon: Double Reinforcement Learning in Infinite-Horizon Processes (2019, background): “This kind of double robustness is sometimes called model double robustness (Smucler et al., 2019) because the rates needed essentially correspond to parametric estimation and therefore the conditions refer to whether these parametric models are well-speciﬁed.”