Tie-breaker experimental designs are hybrids of Randomized Controlled Trials (RCTs) and Regression Discontinuity Designs (RDDs) in which subjects with moderate scores are placed in an RCT while subjects with extreme scores are deterministically assigned to the treatment or control group. In settings where it is unfair or uneconomical to deny the treatment to the more deserving recipients, the tie-breaker design (TBD) trades off the practical advantages of the RDD with the statistical advantages of the RCT. The practical costs of the randomization in TBDs can be hard to quantify in generality, while the statistical benefits conferred by randomization in TBDs have only been studied under linear and quadratic models. In this paper, we discuss and quantify the statistical benefits of TBDs without using parametric modelling assumptions. If the goal is estimation of the average treatment effect or the treatment effect at more than one score value, the statistical benefits of using a TBD over an RDD are apparent. If the goal is nonparametric estimation of the mean treatment effect at merely one score value, we prove that about 2.8 times more subjects are needed for an RDD in order to achieve the same asymptotic mean squared error. We further demonstrate using both theoretical results and simulations from the Angrist and Lavy (1999) classroom size dataset, that larger experimental radii choices for the TBD lead to greater statistical efficiency.

翻译：断线实验设计是随机控制试验(RCTs)和回归性分解设计(RDDs)的混合体,其中中分的科目在RCT中放置,中分的科目在RCT中,而极端分的科目在确定性上分配给治疗或控制组。在拒绝给予更值得的受体治疗的不公平或不经济的环境下,断线设计(TBD)与RCT的统计优势交换了RDD的实际优势。TBD随机化的实际成本很难笼统地量化,而TBDs随机化带来的统计效益只是在线性模型和二次模型模型模型中研究。在本文中,我们讨论和量化TBDs的统计效益而不使用参数模型假设。如果目标是用一个以上的分数来估计平均治疗效果或治疗效果,那么使用TBDD的统计效益是显而易见的。如果TBDs随机选择的实际成本是非参数估计的,仅仅用一个分数值,那么TBDDs的随机值仅根据线和四级模型模型模型模型模型模型模型进行。我们证明,使用一个比的数值要用2.8倍的数值进一步的数值来证明。