Heterogeneous effect estimation plays a crucial role in causal inference, with applications across medicine and social science. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but there are important theoretical gaps in understanding if and when such methods are optimal. This is especially true when the CATE has nontrivial structure (e.g., smoothness or sparsity). Our work contributes in several main ways. First, we study a two-stage doubly robust CATE estimator and give a generic model-free error bound, which, despite its generality, yields sharper results than those in the current literature. We apply the bound to derive error rates in nonparametric models with smoothness or sparsity, and give sufficient conditions for oracle efficiency. Underlying our error bound is a general oracle inequality for regression with estimated or imputed outcomes, which is of independent interest; this is the second main contribution. The third contribution is aimed at understanding the fundamental statistical limits of CATE estimation. To that end, we propose and study a local polynomial adaptation of double-residual regression. We show that this estimator can be oracle efficient under even weaker conditions, if used with a specialized form of sample splitting and careful choices of tuning parameters. These are the weakest conditions currently found in the literature, and we conjecture that they are minimal in a minimax sense. We go on to give error bounds in the non-trivial regime where oracle rates cannot be achieved. Some finite-sample properties are explored with simulations.

翻译：异质性效应估计在因果推断中具有关键作用，广泛应用于医学和社会科学领域。近年来虽涌现出众多条件平均处理效应（CATE）的估计方法，但关于此类方法最优性的理论认知仍存在重要空白——尤其当CATE具有非平凡结构（如光滑性或稀疏性）时。本研究的主要贡献体现在以下几个方面：首先，我们研究了一种两阶段双重稳健CATE估计器，并给出无模型通用误差界。该误差界虽具普适性，却比现有文献结果更为紧致。通过该误差界，我们推导出光滑或稀疏非参数模型的误差率，并给出达到先知效率的充分条件。支撑该误差界的是一类面向含估计或插补结果回归的通用先知不等式——该成果本身具有独立学术价值，此为本研究的第二项主要贡献。第三项贡献旨在揭示CATE估计的统计极限：我们提出并研究了双重残差回归的局部多项式改进方案。研究表明，若配合特定样本分割策略与精心调整的调参参数，该估计器可在更宽松条件下实现先知效率。这些条件当前为文献中最弱者，我们推测其在极小极大意义下具有最小性。进一步地，本文给出了无法达到先知率情形下的误差界，并通过仿真实验探索了部分有限样本性质。