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

This paper examines regression-adjusted estimation and inference of unconditional quantile treatment ei¬€ects (QTEs) under covariate-adaptive randomizations (CARs). Datasets from i¬ eld experiments 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. We establish the consistency, limit distribution, and validity of the multiplier bootstrap of the QTE estimator under CARs. The auxiliary regression may be estimated parametrically, nonparametrically, or via regularization when the data are high-dimensional. Even when the auxiliary regression is misspecii¬ ed, the proposed bootstrap inferential procedure still achieves the nominal rejection probability in the limit under the null. When the auxiliary regression is correctly specii¬ ed, the regression-adjusted estimator achieves the minimum asymptotic variance. We also derive the optimal pseudo true values for the potentially misspecii¬ ed parametric model that minimize the asymptotic variance of the corresponding QTE estimator. Our estimation and inferential methods can be implemented without tuning parameters and they allow for common choices of auxiliary regressions such as linear, probit and logit regressions despite the fact that these regressions may be misspecii¬ ed. Finite-sample performance of the new estimation and inferential methods is assessed in simulations and an empirical application studying the impact of child health and nutrition on educational outcomes is included.