通过在不完全合规的 Covica-Addd性随机化中回归调整提高估计效率 (Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance)

from arxiv, The paper is previously circulated under the title "Regression Adjustments under Covariate-Adaptive Randomizations with Imperfect Compliance."

We study how to improve efficiency via regression adjustments with additional covariates under covariate-adaptive randomizations (CARs) when subject compliance is imperfect. We first establish the semiparametric efficiency bound for the local average treatment effect (LATE) under CARs. Second, we develop a general regression-adjusted LATE estimator which allows for parametric, nonparametric, and regularized adjustments. Even when the adjustments are misspecified, our proposed estimator is still consistent and asymptotically normal, and their inference method still achieves the exact asymptotic size under the null. When the adjustments are correctly specified, our estimator achieves the semiparametric efficiency bound. Third, we derive the optimal linear adjustment that leads to the smallest asymptotic variance among all linear adjustments. We then show the commonly used two stage least squares estimator is not optimal in the class of LATE estimators with linear adjustments while Ansel, Hong, and Li's (2018) estimator is. Fourth, we show how to construct a LATE estimator with nonlinear adjustments which is more efficient than those with the optimal linear adjustment. Fifth, we give conditions under which LATE estimators with nonparametric and regularized adjustments achieve the semiparametric efficiency bound. Last, simulation evidence and empirical application confirm efficiency gains achieved by regression adjustments relative to both the estimator without adjustment and the standard two-stage least squares estimator.

翻译：我们研究如何通过回归调整来提高效率。当对象的合规性不完善时,我们研究如何在共变调整随机(CARs)下通过额外的共变调差来提高效率。我们首先在CARs下为当地平均处理效果(LATE)建立半参数效率。其次, 我们开发一个通用的回归调整 LATE 估计值, 允许参数性、非参数性和正常调整。即使调整定义错误, 我们提议的估计值仍然一致, 且不那么正常, 它们的推断法仍然在无效情况下达到精确的无症状大小。当调整得到正确指定时, 我们的估测器将实现常规半对准处理效果(LATE ) 。第三, 我们得出最佳线性调整, 导致所有线性调整之间最小的无偏差值差异。然后我们展示通常使用的两个阶段最小正方位估计值的估算值不是最佳的等级, 而Ansel, Hong, 和Li18 估测算法则仍然达到无效的大小。第四, 我们展示如何构建一个不精确的平比平面调整法调整法调整, 我们通过不精确的调整, 最终的调整, 我们通过不精确的调整, 将最终的调整, 实现这些调整, 我们通过不精确的对等比平比的平比的平比的平比的平比的平比的平比的平比的平局的平变的调整, 平变的调整, 我们的平比的平变的对的平的的平局性调整, 平的平的平的平的对的平局性调整。