Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra covariates in addition to the strata indicators. We propose to incorporate these additional covariates via auxiliary regressions in the estimation and inference of unconditional quantile treatment effects (QTEs) under CARs. We establish the consistency and limit distribution of the regression-adjusted QTE estimator and prove that the use of multiplier bootstrap inference is non-conservative 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 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 discuss forms of adjustments that can improve the efficiency of the QTE estimators. The finite sample performance of the new estimation and inferential methods is studied in simulations and an empirical application to a well-known dataset concerned with expanding access to basic bank accounts on savings is reported.

翻译：以共变适应随机化(CARs)进行的实地实验产生的数据集通常除层次指标外还包含额外的共变值。我们提议通过辅助回归法将这些额外的共变值纳入CARs下的无条件四分处理效应的估计和推论中。我们确定回归调整后QTE估计值的一致性和限制分布,并证明在CARs下使用倍增靴带突变率是非保守性的。辅助回归法可能是对称性、非对称性的估计,或者在数据高度时通过正规化进行估计。即使辅助回归法被错误地描述,拟议的靴带推断程序仍然在无效的限度下达到名义拒绝概率。当辅助回归法被正确指定时,回归调整后估计值达到最小的反观性差异。我们还讨论能够提高QTE估计器效率的调整形式。在模拟中研究新估算法和推论方法的有限样本性表现,并报告对银行基本储蓄账户进行实验性应用。