AI 中文总结
该研究开发去偏机器学习通用框架，通过矩条件识别参数$\theta_0$，利用机器学习估计干扰项$\gamma_0$并校正偏差。建立里斯表示器$\alpha_0$的识别条件，开发通用估计程序，纳入形状约束提高精度，通过模拟和实证应用展示方法。
AI 中文摘要
我们开发了一个用于自动去偏机器学习（DML）的识别和估计通用框架，其中感兴趣的参数$\theta_0$通过涉及可能是高维干扰项$\gamma_0$的矩条件来识别。DML利用机器学习估计$\gamma_0$，同时校正可能会传递到$\theta_0$的有偏估计的正则化和过拟合偏差。我们建立了DML核心的里斯表示器$\alpha_0$被识别的条件，并表明当$\alpha_0$唯一优化一个二次泛函时恰好发生识别。这一特性使我们能够为$\alpha_0$开发一个通用估计程序，该程序适用于一般的$\gamma_0$，包括由具有内生性的模型定义的那些，并涵盖经典筛法和现代架构如深度神经网络。为了提高估计精度并减轻维度诅咒，我们通过将$\gamma_0$嵌入到一个可能的非线性参数空间中来纳入形状约束。我们通过模拟和实证应用说明了我们的估计程序。
英文摘要
We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest $θ_0$ is identified by a moment condition involving a nuisance $γ_0$ that may be high dimensional. We establish conditions under which the Riesz representer $α_0$, which is at the core of DML, is identified, and show that the identification occurs precisely when $α_0$ uniquely optimizes a quadratic functional. This characterization enables us to develop a general estimation procedure for $α_0$ that allows for generic $γ_0$ including those defined by models with endogeneity and encompasses both classical sieves and modern architectures such as deep neural networks. To improve estimation precision and mitigate the curse of dimensionality, we incorporate shape constraints on $γ_0$ by embedding them into a possibly nonlinear parameter space. We illustrate our estimation procedure through simulations and empirical applications.
