We study regression adjustment with general function class approximations for estimating the average treatment effect in the design-based setting. Standard regression adjustment involves bias due to sample re-use, and this bias leads to behavior that is sub-optimal in the sample size, and/or imposes restrictive assumptions. Our main contribution is to introduce a novel decorrelation-based approach that circumvents these issues. We prove guarantees, both asymptotic and non-asymptotic, relative to the oracle functions that are targeted by a given regression adjustment procedure. We illustrate our method by applying it to various high-dimensional and non-parametric problems, exhibiting improved sample complexity and weakened assumptions relative to known approaches.

翻译：我们研究了基于设计框架下，使用一般函数类逼近进行回归调整以估计平均处理效应的问题。标准回归调整因样本重复使用而产生偏差，这种偏差导致样本量效率欠佳且/或需施加严格假设。本文的主要贡献是提出一种新颖的去相关方法，有效规避了上述问题。我们证明了该方法相对于给定回归调整程序所目标的神谕函数，具有渐近与非渐近双重保证。通过将方法应用于多种高维与非参数问题，我们展示了相较于现有方法更优的样本复杂度与更宽松的假设条件。