Debiased regression adjustment in completely randomized experiments with moderately high-dimensional covariates
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中等高维协变量下完全随机实验的去偏回归调整
- 研究问题
- 在协变量维度可与样本量同阶的完全随机实验中，如何不依赖潜在结果线性表示的稀疏性，实现处理效应估计与有效推断？
- 方法与思路
- 作者在协变量和潜在结果固定、随机性仅来自处理分配的框架下，构造去偏回归调整估计量及相应推断程序。
- 材料陈述的贡献
- 摘要称，新估计量无需稀疏约束，并在一定条件下具有渐近正态性；作者还讨论相对未调整估计量的效率改善并开展数值分析。
- 阅读关注点
- 应核对维度与样本量的具体限制、去偏项和方差估计公式，以及渐近正态性条件和效率改善分别适用的维度范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收未核实；摘要未展开温和假设，维度同阶的表述不能解释为任意维度比例均允许有效推断。
原文摘要
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.