Inference for weighted average derivative effects (WADEs) usually relies on kernel density estimators, which introduce complicated bandwidth-dependant biases. By considering a new class of Riesz representers, we propose WADEs which require estimating conditional expectations only, and derive an optimally efficient WADE, also connected to projection parameters in partially linear models. We derive efficient estimators under the nonparametric model, which are amenable to machine learning of working models. We propose novel learning strategies based on the R-learner strategy. We perform a simulation study and apply our estimators to determine the effect of Warfarin dose on blood clotting function.

翻译：关于加权平均导数效应（WADEs）的推断通常依赖于核密度估计器，这引入了复杂的带宽相关偏差。通过考虑一类新的Riesz表示量，我们提出了仅需估计条件期望的WADEs，并推导出最优高效的WADE，该估计量也与部分线性模型中的投影参数相关联。我们在非参数模型下推导出高效的估计量，这些估计量适用于工作模型的机器学习。我们基于R-learner策略提出了新颖的学习方法。我们进行了模拟研究，并将我们的估计量应用于确定华法林剂量对血液凝血功能的影响。