Ridge Rerandomization：一种存在共线性的试验设计策略
Ridge Rerandomization: An Experimental Design Strategy in the Presence of Collinearity
摘要：
随机化确保观察到的和未观察到的协变量平均平衡。然而，治疗和对照单位的随机化往往会导致协变量的实现不平衡，这种不平衡可能会扩大治疗效果估计量的方差。这个问题的一个解决方案是重新随机化-一种试验设计策略，将单位随机化，直到满足某些平衡标准-如果协变量与结果相关，则产生更精确的治疗效果估计值。文献中的大多数重新随机化方案使用马哈拉诺比斯距离，当协变量相关或重要性不同时，这可能不是最佳方法。作为替代方案，我们引入了一个试验设计策略，称为岭重新随机化，它利用修改后的马哈拉诺比斯距离，解决协变量之间的共线性，并自动放置一个层次的重要性的协变量根据其特征结构。这种修正的马哈拉诺比斯距离与主成分和欧几里得距离有联系，据我们所知，它还没有被探索过。我们建立了几个理论性质的修改后的马哈拉诺比斯距离和我们的岭重新随机化计划。这些结果保证了脊重新随机化优于随机化，并表明脊重新随机化优于标准重新随机化方案。我们还提供了模拟证据表明，脊重新随机化是特别可取的典型的重新随机化方案在高维或高共线性设置。
英文摘要：
Randomization ensures that observed and unobserved covariates are balanced, on average. However, randomizing units to treatment and control often leads to covariate imbalances in realization, and such imbalances can inflate the variance of estimators of the treatment effect. One solution to this problem is rerandomization---an experimental design strategy that randomizes units until some balance criterion is fulfilled---which yields more precise estimators of the treatment effect if covariates are correlated with the outcome. Most rerandomization schemes in the literature utilize the Mahalanobis distance, which may not be preferable when covariates are correlated or vary in importance. As an alternative, we introduce an experimental design strategy called ridge rerandomization, which utilizes a modified Mahalanobis distance that addresses collinearities among covariates and automatically places a hierarchy of importance on the covariates according to their eigenstructure. This modified Mahalanobis distance has connections to principal components and the Euclidean distance, and---to our knowledge---has remained unexplored. We establish several theoretical properties of this modified Mahalanobis distance and our ridge rerandomization scheme. These results guarantee that ridge rerandomization is preferable over randomization and suggest when ridge rerandomization is preferable over standard rerandomization schemes. We also provide simulation evidence that suggests that ridge rerandomization is particularly preferable over typical rerandomization schemes in high-dimensional or high-collinearity settings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
