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Title: Global and local estimators of a dose-response curve Authors:  Matteo Bonvini - Carnegie Mellon University (United States) [presenting]
Edward Kennedy - Carnegie Mellon University (United States)
Abstract: The problem of estimating a dose-response curve, both globally and locally at a point, is considered. Letting $A$ denote a continuous treatment variable, the target of inference is the expected outcome if everyone in the population takes treatment level $A=a$. Under standard assumptions, the dose-response function takes the form of a partial mean. Building upon the recent literature on nonparametric regression with orthogonal signals, we study three different estimators. As a global method, we build upon previous work to construct an empirical-risk-minimization-based estimator and give an explicit characterization of second-order remainder terms. As a local method, we develop a DR-learner. Finally, we construct an $mth$ order estimator based on the theory of higher-order influence functions. For each estimator, we provide an upper bound on the mean-square error and investigate its finite-sample performance in a simulation.