AI 中文总结
该研究提出面向回退实验的扩展CUPED框架，结合多历史滞后项等协变量与交叉拟合，提升方差缩减效率，经模拟和纽约出租车出行数据验证可显著增强统计功效。
AI 中文摘要
基于实验前数据的受控实验方法（CUPED）通过利用实验前滞后值调整实验内的结果指标，可降低在线实验中处理效应估计量的方差。该方法可通过丰富协变量集来增强效果，同时保持自动化特性，防止过拟合和协变量泄露。在回退（switchback）及相关聚类实验设计中，这种协变量集的丰富尤为有效，因为结果的随机化单元层面变异会放大处理效应估计量的方差，因此能解释该变异的协变量可带来不成比例的大效率提升。我们开发了适用于回退及相关聚类设计的扩展CUPED框架，与传统CUPED相比，该框架在保持轻量性且仅采用CUPED隐含假设的前提下，大幅提升了方差缩减效率。该框架在实验前预测模型中结合了多个历史滞后项、每日小时循环编码，以及聚类和小时层面的固定效应虚拟变量——这些协变量针对随机化单元层面的结果变异——并采用交叉拟合，以避免样本内过拟合导致实际方差缩减被高估。在模拟实验中，我们分析了各组件对该方法有效性和效率的影响，结果表明完整框架可显著提升统计功效。我们还在纽约市出租车与豪华轿车委员会公开的出行记录上验证了该方法。最后，我们推导了任意协变量调整可实现的方差缩减的闭式上限，并将实证发现与该上限施加的依赖于构成的限制联系起来。
英文摘要
Controlled-experiment Using Pre-Experiment Data (CUPED) reduces the variance of the treatment effect estimator in online experiments by adjusting the in-experiment outcome metric using its lagged pre-experiment value. This method can be strengthened by enriching its covariate set while keeping it automatable and guarding against overfitting and covariate leakage. In switchback and related clustered experiment designs, this enrichment may be especially fruitful since randomization-unit-level variation in the outcome amplifies the variance of the treatment effect estimator, so covariates that explain it yield disproportionately large efficiency gains. We develop an extended CUPED framework for switchback and related clustered designs that introduces sizeable improvement in variance reduction efficiency relative to conventional CUPED while remaining lightweight and free of assumptions beyond those already implicit in CUPED. The framework combines multiple historical lags with cyclic hour-of-day encodings and cluster- and hour-level fixed-effect dummies in the pre-period prediction model---covariates that target randomization-unit-level outcome variation---and uses cross-fitting so that realized variance reduction is not inflated by in-sample overfitting. In simulation, we analyze how each component affects validity and efficiency of this method and show that the full framework yields large gains in statistical power. We further validate the approach on publicly available trip records from the New York City Taxi and Limousine Commission. Finally, we derive a closed-form ceiling on the variance reduction attainable by any covariate adjustment and connect our empirical findings to the composition-dependent limits this ceiling imposes.
