  Single-parameter summaries of variable effects are desirable for ease of
interpretation, but linear models, which would deliver these, may fit poorly to
the data. A modern approach is to estimate the average partial effect -- the
average slope of the regression function with respect to the predictor of
interest -- using a doubly robust semiparametric procedure. Most existing work
has focused on specific forms of nuisance function estimators. We extend the
scope to arbitrary plug-in nuisance function estimation, allowing for the use
of modern machine learning methods which in particular may deliver
non-differentiable regression function estimates. Our procedure involves
resmoothing a user-chosen first-stage regression estimator to produce a
differentiable version, and modelling the conditional distribution of the
predictors through a location-scale model. We show that our proposals lead to a
semiparametric efficient estimator under relatively weak assumptions. Our
theory makes use of a new result on the sub-Gaussianity of Lipschitz score
functions that may be of independent interest. We demonstrate the attractive
numerical performance of our approach in a variety of settings including ones
with misspecification.
