Finite-Sample Guarantees for High-Dimensional DML
This work offers incremental improvements for applied researchers in causal inference by providing finite-sample bounds to assess confidence band accuracy in high-dimensional settings.
The paper provides finite-sample guarantees for high-dimensional debiased machine learning (DML) estimators, bounding the deviation of their finite-sample distribution from the asymptotic Gaussian approximation to inform confidence band coverage. It addresses joint inference for high-dimensional causal parameters, such as multiple treatment effects or impacts on entire distributions.
Debiased machine learning (DML) offers an attractive way to estimate treatment effects in observational settings, where identification of causal parameters requires a conditional independence or unconfoundedness assumption, since it allows to control flexibly for a potentially very large number of covariates. This paper gives novel finite-sample guarantees for joint inference on high-dimensional DML, bounding how far the finite-sample distribution of the estimator is from its asymptotic Gaussian approximation. These guarantees are useful to applied researchers, as they are informative about how far off the coverage of joint confidence bands can be from the nominal level. There are many settings where high-dimensional causal parameters may be of interest, such as the ATE of many treatment profiles, or the ATE of a treatment on many outcomes. We also cover infinite-dimensional parameters, such as impacts on the entire marginal distribution of potential outcomes. The finite-sample guarantees in this paper complement the existing results on consistency and asymptotic normality of DML estimators, which are either asymptotic or treat only the one-dimensional case.