Conditional Influence Functions

原文摘要

There are many nonparametric objects of interest that are functionals of a conditional distribution, such as average treatment effects conditional on a low-dimensional set of covariates. We define a conditional influence function (CIF) as the Gateaux derivative of a conditional parameter with respect to perturbations of the conditional law of a single observation given the conditioning variable. CIFs generalize classical influence functions and can be used to (i) construct Neyman-orthogonal conditional moment equations for parameters that depend on high-dimensional nuisance functions, (ii) quantify local sensitivity to misspecification and local policy effects, and (iii) build debiased estimators of conditional parameters via nonparametric regression of cross-fit pseudo-outcomes on the conditioning variable. We derive CIFs for a broad class of parameters that are linear functionals of conditional means and extend the analysis to parameters depending on general features of conditional distributions defined by convex conditional M-estimation. For locally linear second-stage estimation, we give rate conditions under which first-stage machine learning has no first-order impact on the asymptotic distribution and we provide implementable standard errors.

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