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.

翻译：完全随机实验是因果推断的黄金标准。当每个实验候选对象的协变量信息可用时，一种典型做法是将它们纳入协变量调整，以更准确地估计处理效应。本文在随机化框架下研究该问题，即所有实验候选对象的协变量和潜在结果被视为确定性量，随机性仅来源于处理分配机制。在此框架下，为实现渐近有效的推断，现有估计量通常要求以下两者之一：（i）协变量维度 $p$ 的增速不超过 $O(n^{2/3})$（样本量 $n \to \infty$）；或（ii）基于可能高维协变量构建的潜在结果线性表示满足特定稀疏性约束。本文考虑中等高维情形，允许 $p$ 与 $n$ 处于相同量级。我们提出一种新型去偏估计量及其相应推断程序，并在温和假设下建立其渐近正态性。该估计量无需模型假设，且不对潜在结果的线性表示施加任何稀疏性约束。我们还讨论了在不同维度约束下，其相对于未调整处理效应估计量的渐近效率提升。数值分析表明，与其他基于回归调整的处理效应估计量相比，本文提出的去偏估计量在中等高维场景下表现良好。