Optimally weighted average derivative effects

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.