Finite-Sample Guarantees for High-Dimensional DML

TL;DR

This paper provides finite-sample bounds for high-dimensional debiased machine learning estimators, enhancing understanding of their accuracy and coverage in practical, finite-sample scenarios for causal inference.

Contribution

It introduces novel finite-sample guarantees for joint inference in high-dimensional DML, extending beyond asymptotic results to multi-dimensional and infinite-dimensional parameters.

Findings

Finite-sample bounds quantify deviation from Gaussian approximation.

Guarantees inform about coverage accuracy of confidence bands.

Applicable to various high-dimensional causal parameters.

Abstract

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.