Semiparametric Counterfactual Density Estimation

Abstract Causal effects are often characterized with averages, which can give an incomplete picture of the underlying counterfactual distributions. Here we consider estimating entire density and generic functionals thereof. We focus on two kinds target parameters: approximations distance between densities. study nonparametric efficiency bounds, giving results for smooth but otherwise models distances. Importantly, show how these bounds connect to means particular nontrivial functions counterfactuals, linking problems mean estimation. propose doubly robust-style estimators, their rates convergence, showing that they be optimally efficient in large models. also analogous methods model selection aggregation, when many may available interest. Our all hold distances, highlight L2 projections linear KL exponential families. Finally, illustrate our method by CD4 count among patients HIV, had been treated combination therapy versus zidovudine alone, as well a effect. implemented R package npcausal GitHub.