Minimax Optimal Nonparametric Estimation of Heterogeneous Treatment Effects
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A central goal of causal inference is to detect and estimate the treatment effects of a given treatment or intervention on an outcome variable of interest, where a member known as the heterogeneous treatment effect (HTE) is of growing popularity in recent practical applications such as the personalized medicine. In this paper, we model the HTE as a smooth nonparametric difference between two less smooth baseline functions, and determine the statistical limits of the nonparametric HTE estimation. Specifically, we construct the HTE estimators via a novel combination of kernel methods and covariate matching under both fixed and random designs, and show that the estimation performance is characterized by an interpolation between the smoothness parameters determined by the matching quality and the noise level. We also establish the optimality of the above estimators with matching minimax lower bounds.
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