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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 accuratetreatment effect estimation. In this paper, we investigate this problem underthe randomization-based framework, i.e., that the covariates and potentialoutcomes of all experimental candidates are assumed as deterministic quantitiesand the randomness comes solely from the treatment assignment mechanism. Underthis framework, to achieve asymptotically valid inference, existing estimatorsusually require either (i) that the dimension of covariates $p$ grows at a rateno faster than $O(n^{2 / 3})$ as sample size $n \to \infty$; or (ii) certainsparsity constraints on the linear representations of potential outcomesconstructed via possibly high-dimensional covariates. In this paper, weconsider the moderately high-dimensional regime where $p$ is allowed to be inthe same order of magnitude as $n$. We develop a novel debiased estimator witha corresponding inference procedure and establish its asymptotic normalityunder mild assumptions. Our estimator is model-free and does not require anysparsity constraint on potential outcome's linear representations. We alsodiscuss its asymptotic efficiency improvements over the unadjusted treatmenteffect estimator under different dimensionality constraints. Numerical analysisconfirms that compared to other regression adjustment based treatment effectestimators, our debiased estimator performs well in moderately high dimensions.

Debiased Regression Adjustment in Completely Randomized Experiments with Moderately High-dimensional Covariates