AI 中文总结
本文针对低维SAR参数，提出结合算子正交SAR-IV/GMM得分与缓冲空间交叉拟合的双重/去偏机器学习推断方法，解决空间权重矩阵未知、函数形式不稳健及特征内生问题，经模拟和美国糖尿病应用验证了方法的有效性。
AI 中文摘要
空间自回归（SAR）推断通常以空间权重矩阵W为条件，尽管潜在的交互结构往往未知，且实证结论可能对其设定敏感。本文针对低维SAR参数开发了双重/去偏机器学习推断方法，其中空间交互算子可从潜在内生特征中灵活学习。在维持的容许支撑内，交互强度由地理和社会经济特征的未知函数生成，使得推断对该支撑内权重的函数形式设定具有稳健性。生成W的特征中的内生性通过基于局部相关第一阶段残差信息的非线性控制函数解决。由于学习到的算子同时进入空间滞后和空间变换工具变量，将估计的W视为已知通常会产生一阶生成W效应。本文构建了算子正交的SAR-IV/GMM得分，以消除这种主导敏感性，并结合缓冲空间交叉拟合，将评估得分足迹与干扰训练观测值分离。在空间混合创新场的近 epoch 依赖性、目标相关干扰率和正则性条件下，该估计量渐近线性且服从根-n正态分布。蒙特卡洛模拟显示，当交互函数设定错误、生成权重的特征内生且观测值空间相关时，与非正交替代方法相比，本文方法的有限样本推断性能更优。在美国的应用中，糖尿病相关估计值随W的选择而变化，表明SAR推断对交互结构的敏感性；即使对于相同的学习W，不同推断方法的结果也存在差异，凸显了学习W时推断的重要性。
英文摘要
Spatial autoregressive inference is typically conditional on the spatial weights matrix, W, even though the underlying interaction structure is often unknown and empirical conclusions can be sensitive to its specification. This paper develops double/debiased machine learning inference for low-dimensional SAR parameters when the spatial interaction operator is learned flexibly from potentially endogenous characteristics. Within a maintained admissible support, interaction strength is generated by an unknown function of geographic and socioeconomic characteristics, making inference robust to functional form specification of the weights within that support. Endogeneity in the characteristics generating W is addressed through a nonlinear control function based on locally relevant first-stage residual information. Because the learned operator enters both the spatial lag and spatially transformed instruments, treating the estimated W as known generally leaves a first-order generated-W effect. I construct an operator-orthogonal SAR-IV/GMM score that removes this leading sensitivity and combine it with buffered spatial cross-fitting that separates evaluation-score footprints from nuisance-training observations. Under near epoch dependence on a spatially mixing innovation field and target-relevant nuisance rate and regularity conditions, the estimator is asymptotically linear and root-n normal. Monte Carlo simulations show improved finite-sample inference relative to nonorthogonal alternatives when the interaction function is misspecified, weight generating characteristics are endogenous, and observations are spatially dependent. In a U.S. application, diabetes estimates vary with the choice of W, showing the sensitivity of SAR inference to the interaction structure. Even for the same learned W, results differ across inferential methods, highlighting the importance of inference when W is learned.
