Abstract: We propose a regularized projection score method for estimating the treatment effects in a quantile regression in the presence of high-dimensional confounding covariates. We show that the proposed estimator of the treatment effects is consistent and asymptotically normal, with a root-𝓃 rate of convergence. We also provide an efficient algorithm for the proposed estimator. This algorithm can be implemented easily using existing software. Furthermore, we propose and validate a refitted wild bootstrapping approach for variance estimation. This enables us to construct confidence intervals for the treatment effects in high-dimensional settings. Simulation studies are carried out to evaluate the finite-sample performance of the proposed estimator. A GDP growth rate data set is used to demonstrate an application of the method.

Key words and phrases: Efficiency score, high dimension, quantile regression, wild bootstrap.