  Continuous treatments (e.g., doses) arise often in practice, but many
available causal effect estimators are limited by either requiring parametric
models for the effect curve, or by not allowing doubly robust covariate
adjustment. We develop a novel kernel smoothing approach that requires only
mild smoothness assumptions on the effect curve, and still allows for
misspecification of either the treatment density or outcome regression. We
derive asymptotic properties and give a procedure for data-driven bandwidth
selection. The methods are illustrated via simulation and in a study of the
effect of nurse staffing on hospital readmissions penalties.
