Sparsity Double Robust Inference of Average Treatment Effects

TL;DR

This paper introduces a new method for estimating average treatment effects that provides valid confidence intervals in high-dimensional settings, requiring only one of the response surface or treatment probability to be ultra-sparse, thus broadening applicability.

Contribution

The authors propose a novel inference method that achieves asymptotic exactness under weaker sparsity assumptions, improving robustness over existing approaches.

Findings

Method yields asymptotically exact confidence intervals.

Valid under ultra-sparsity in either response surface or treatment model.

Results are semi-parametrically efficient.

Abstract

Many popular methods for building confidence intervals on causal effects under high-dimensional confounding require strong "ultra-sparsity" assumptions that may be difficult to validate in practice. To alleviate this difficulty, we here study a new method for average treatment effect estimation that yields asymptotically exact confidence intervals assuming that either the conditional response surface or the conditional probability of treatment allows for an ultra-sparse representation (but not necessarily both). This guarantee allows us to provide valid inference for average treatment effect in high dimensions under considerably more generality than available baselines. In addition, we showcase that our results are semi-parametrically efficient.