  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 $p$ grows at a rate
no faster than $O(n^{2 / 3})$ as sample size $n \to \infty$; 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.
