Doubly-robust inference and optimality in structure-agnostic models with smoothness
带平滑性约束的结构无关模型中的双重稳健推断与最优性AI 解读 ↓
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带平滑性约束的结构无关模型中的双重稳健推断与最优性
- 研究问题
- 在仅掌握辅助函数估计误差且增加平滑性约束时，能否改进 ATE 估计的最优收敛率，并在部分辅助函数估计不一致时保持有效推断？
- 方法与思路
- 作者定义结合结构无关性与平滑约束的分布类，推导 ATE 的极小极大下界，并构造具有双重稳健渐近线性性质的新估计器。
- 材料陈述的贡献
- 摘要称在特定条件下，新方法可支持部分辅助函数估计不一致或较慢时的 Wald 推断，并较 AIPW 更快且达到所述下界速率。
- 阅读关注点
- 应核对新分布类的平滑性限制、下界适用范围，以及双重稳健渐近线性所需条件，明确何时能够获得速率改进和有效区间。
- 阅读边界
- 所给版本为 arXiv 预印本，不能据此认定已同行评审或获期刊接收；摘要未列出具体平滑度、误差率及定理条件，不能泛化为无条件优于 AIPW。
原文摘要
We study the problem of constructing an estimator of the average treatment effect (ATE) with observational data. The celebrated doubly-robust, augmented-IPW (AIPW) estimator generally requires consistent estimation of both nuisance functions for standard root-n inference, and moreover that the product of the errors of the nuisances should shrink at a rate faster than $n^{-1/2}$. A recent strand of research has aimed to understand the extent to which the AIPW estimator can be improved upon (in a minimax sense). Under structural assumptions on the nuisance functions, the AIPW estimator is typically not minimax-optimal, and improvements can be made using higher-order influence functions (Robins et al, 2017). Conversely, without any assumptions on the nuisances beyond the mean-square-error rates at which they can be estimated, the rate achieved by the AIPW estimator is already optimal (Balakrishnan et al, 2023; Jin and Syrgkanis, 2024). We make three main contributions. First, we propose a new hybrid class of distributions that combine structural agnosticism regarding the nuisance function space with additional smoothness constraints. Second, we calculate minimax lower bounds for estimating the ATE in the new class, as well as in the pure structure-agnostic one. Third, we propose a new estimator of the ATE that enjoys doubly-robust asymptotic linearity; it can yield asymptotically valid Wald-type confidence intervals even when the propensity score or the outcome model is inconsistently estimated, or estimated at a slow rate. Under certain conditions, we show that its rate of convergence in the new class can be much faster than that achieved by the AIPW estimator and, in particular, matches the minimax lower bound rate, thereby establishing its optimality. Finally, we complement our theoretical findings with simulations.