Debiased regression adjustment in completely randomized experiments with moderately high-dimensional covariates

TL;DR

This paper introduces a new debiased regression adjustment method for causal effect estimation in randomized experiments with high-dimensional covariates, achieving valid inference without sparsity assumptions.

Contribution

It develops a novel, model-free debiased estimator that works in the moderately high-dimensional regime where covariate dimension is comparable to sample size, without requiring sparsity.

Findings

Estimator is asymptotically normal under mild conditions

Performs well in simulations compared to existing methods

Improves efficiency over unadjusted estimators in high dimensions

Abstract

Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment effect estimation. In this paper, we investigate this problem under the randomization-based framework, i.e., that the covariates and potential outcomes of all experimental candidates are assumed as deterministic quantities and the randomness comes solely from the treatment assignment mechanism. Under this framework, to achieve asymptotically valid inference, existing estimators usually require either (i) that the dimension of covariates $p$ is much smaller than the sample size $n$; or (ii) certain sparsity constraints on the linear representations of potential outcomes constructed via possibly high-dimensional covariates. In this paper, we consider the moderately high-dimensional regime where $p$ is allowed to be in the same order of magnitude as $n$. We develop a novel debiased estimator with a corresponding inference procedure and establish its asymptotic normality under mild assumptions. Our estimator is model-free and does not require any sparsity constraint on potential outcome's linear representations. We also discuss its asymptotic efficiency improvements over the unadjusted treatment effect estimator under different dimensionality constraints. Numerical analysis confirms that compared to other regression adjustment based treatment effect estimators, our debiased estimator performs well in moderately high dimensions.