提出自适应超参数选择方法，解决因果模型中未知平滑性导致的估计不稳问题。
Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principle
- 基于偏差-方差权衡原理，自动调整正则化参数，无需预先知道函数平滑度。
- 在弱度量和强度量下均达到最优收敛速度，适用于RDIV和TRAE等模型。
- 构建全自适应双重稳健估计器，适合实际应用中的因果推断与理论分析。
我们研究由条件矩约束定义的不适定线性逆问题中的自适应估计与推断。现有正则化估计器如正则化深度工具变量（RDIV）需事先知晓干扰函数的平滑性，通常通过贝塔源条件设定正则化参数。但在实践中该平滑性未知，参数误设会导致收敛性能下降或不稳定。本文提出基于偏差原则的自适应超参数选择框架，无需依赖未知平滑参数即可自动平衡偏差与方差。该框架适用于RDIV（Li等，2024）和蒂科诺夫正则化对抗估计器（TRAE）（Bennett等，2023a），并在弱度量和强度量下均实现最优率。在此基础上，我们构建了一个完全自适应的双重稳健估计器，用于线性泛函估计，其速率可达更优条件下的原始或对偶问题最优水平，为不适定计量模型中的自适应推断提供了实用且理论坚实的方法。
原文摘要 · Abstract (English)
We study adaptive estimation and inference in ill-posed linear inverse problems defined by conditional moment restrictions. Existing regularized estimators such as Regularized DeepIV (RDIV) require prior knowledge of the smoothness of the nuisance function, typically encoded by a beta source condition to tune their regularization parameters. In practice, this smoothness is unknown, and misspecified hyperparameters can lead to suboptimal convergence or instability. We introduce a discrepancy-principle-based framework for adaptive hyperparameter selection that automatically balances bias and variance without relying on the unknown smoothness parameter. Our framework applies to both RDIV (Li et al. [2024]) and the Tikhonov Regularized Adversarial Estimator (TRAE) (Bennett et al. [2023a]) and achieves the same rates in both weak and strong metrics. Building on this, we construct a fully adaptive doubly robust estimator for linear functionals that attains the optimal rate of the better-conditioned primal or dual problem, providing a practical, theoretically grounded approach for adaptive inference in ill-posed econometric models.
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