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.

翻译：使用共变适应随机化(CARs)的实地实验的数据集通常包含额外的基线共变数,除了层次指标之外,还包含额外的基准共变数。我们提议通过辅助回归法将这些额外共变数纳入CARs下的无条件QTEs的估计和推论中。我们确定回归调整 QTE 估测器的倍增靴带的一致性、限制分布和有效性。辅助回归法可能是从参数上估算,不是对等的,或者当数据为高维度时通过正规化。即使辅助回归法被错误地描述,拟议的靴子陷阱推断程序仍然在无效限度下达到名义拒绝概率。当辅助回归法被正确指定时,回归调整的估测器达到最小的负值差异。我们还为可能错误地定义的参数模型得出了最佳的假真实值,以尽量减少相应的QTE 估测器的不相称性差异。我们用模拟法展示了新估算和推论方法的有限样本性性表现,并为教育中众所周知的数据集提供了实验应用提供实验性应用。