Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations

Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra baseline covariates in addition to the strata indicators. We propose to incorporate these extra covariates via auxiliary regressions in the estimation and inference of unconditional QTEs under CARs. We establish the consistency, limiting distribution, and validity of the multiplier bootstrap of the regression-adjusted QTE estimator. The auxiliary regression may be estimated parametrically, nonparametrically, or via regularization when the data are high-dimensional. Even when the auxiliary regression is misspecified, the proposed bootstrap inferential procedure still achieves the nominal rejection probability in the limit under the null. When the auxiliary regression is correctly specified, the regression-adjusted estimator achieves the minimum asymptotic variance. We also derive the optimal pseudo true values for the potentially misspecified parametric model that minimize the asymptotic variance of the corresponding QTE estimator. We demonstrate the finite sample performance of the new estimation and inferential methods using simulations and provide an empirical application to a well-known dataset in education.