论文标题
模式治疗效果
The Mode Treatment Effect
论文作者
论文摘要
平均值，中值和模式是概率分布中心性的三个基本措施。在计划评估中，在过去的几十年中，对平均治疗效果（平均）和分位数治疗效果（中值）进行了深入研究。但是，在计划评估中，长期以来一直忽略了模式治疗效果。本文通过讨论模式治疗效果的估计和推断来填补空白。我提出了传统的内核和机器学习方法来估计模式治疗效果。我还得出了所提出的估计器的渐近性能，发现两个估计量都遵循渐近正态性，但收敛速率慢于常规速率$ \ sqrt {n} $，这与经典平均值和分数处理效应估计器的速率不同。
Mean, median, and mode are three essential measures of the centrality of probability distributions. In program evaluation, the average treatment effect (mean) and the quantile treatment effect (median) have been intensively studied in the past decades. The mode treatment effect, however, has long been neglected in program evaluation. This paper fills the gap by discussing both the estimation and inference of the mode treatment effect. I propose both traditional kernel and machine learning methods to estimate the mode treatment effect. I also derive the asymptotic properties of the proposed estimators and find that both estimators follow the asymptotic normality but with the rate of convergence slower than the regular rate $\sqrt{N}$, which is different from the rates of the classical average and quantile treatment effect estimators.
