This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine learning tools. We represent this structural function as a conditional expectation of an unbiased signal that depends on a nuisance parameter, which we estimate by modern machine learning techniques. We first adjust the signal to make it insensitive (Neyman-orthogonal) with respect to the first-stage regularisation bias. We then project the signal onto a set of basis functions, which grow with sample size, to get the best linear predictor of the structural function. We derive a complete set of results for estimation and simultaneous inference on all parameters of the best linear predictor, conducting inference by Gaussian bootstrap. When the structural function is smooth and the basis is sufficiently rich, our estimation and inference results automatically target this function. When basis functions are group indicators, the best linear predictor reduces to the group average treatment/structural effect, and our inference automatically targets these parameters. We demonstrate our method by estimating uniform confidence bands for the average price elasticity of gasoline demand conditional on income.

中文翻译：

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条件平均治疗效果和其他因果函数的去偏机器学习

本文提供了基于现代机器学习工具的结构函数的最佳线性预测器（近似值）的估计和推理方法，例如条件平均结构和处理效果以及结构导数。我们将此结构函数表示为依赖于干扰参数的无偏信号的条件期望，我们通过现代机器学习技术对其进行估计。我们首先调整信号以使其对第一阶段正则化偏差不敏感（Neyman 正交）。然后我们将信号投影到一组随样本大小增长的基函数上，以获得结构函数的最佳线性预测器。我们推导出一套完整的结果，用于对最佳线性预测器的所有参数进行估计和同时推断，通过高斯引导进行推理。当结构函数平滑且基础足够丰富时，我们的估计和推理结果会自动针对该函数。当基函数是组指标时，最佳线性预测器会降低到组平均处理/结构效果，我们的推断会自动针对这些参数。我们通过估计以收入为条件的汽油需求平均价格弹性的统一置信区间来证明我们的方法。我们的推理会自动针对这些参数。我们通过估计以收入为条件的汽油需求平均价格弹性的统一置信区间来证明我们的方法。我们的推理会自动针对这些参数。我们通过估计以收入为条件的汽油需求平均价格弹性的统一置信区间来证明我们的方法。