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Abstract:
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Individuals do not only differ in their innate characteristics but also in how they respond to a particular treatment or intervention. Quantile regression, which model the effect of covariates on the conditional distribution of the response variable, provide a natural approach to study such heterogeneous treatment effects. In this talk, we propose a framework for inference of a possibly infinite collection of quantile treatment effect curves in the presence of high-dimensional covariates. Our method combines a de-biased L1-penalized regression adjustment with a quantile-specific balancing scheme which underlies a bias-variance trade-off. By choosing the balancing weights such that they minimize the variance and suppress the bias, we no longer require the covariates distribution to overlap, i.e. the propensity score to be uniformly bounded away from zero and one. We show weak convergence of the proposed estimator to a Gaussian process whose finite dimensional covariance function can be consistently estimated under mild conditions. We discuss the merits of our method and provide finite-sample performances in a variety of settings.
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