Topics in Threshold Models: Efficient Procedures under Endogeneity in Regression Discontinuity Designs and Distributed and Robust Estimation of Change-Points

该项目涉及两种不同的挑战。第一个挑战涉及一类回归不连续设计，其中的问题是，是否一种待遇，如助学金、奖学金或被一个有利可图的项目接受，是否直接影响结果，例如，学生未来的收入。困难在于，这种治疗恰恰是针对那些预计会有更好结果的人。因此，很难区分治疗是否产生了影响，或者只是简单地说，更好的候选人得到了影响。一种标准的方法只使用接近门槛的学生的数据，将那些勉强获得奖学金的学生与略低于门槛的学生进行比较。项目中考虑的方法使用了所有的数据。该项目中的第二个问题涉及观测值的分布突然改变的情况。例如，如果环境中的感染剂类型发生了变化，就可能发生这种情况。该项目的主要关注点是，当在不同的地点监测这种变化时，在每个地点，变化几乎同时发生。然而，由于隐私或交通问题，我们需要严格限制从每个站点传递到中央控制的信息量。该项目处理几类问题的新估计和推理技术，这些问题表现出一维或多维的不连续性作为感兴趣的关键特征。所研究的问题提出了两种不同的挑战：第一类是确定一类回归不连续设计(RDD)模型中是否存在明显的处理效果，其中处理组由一个核心协变量的预先设定的阈值确定。模型将通过引入新的估计方程的新观点来解决，该新的估计方程允许统计学家利用手头的全部数据来提出在存在内生性的情况下对治疗效果的半参数有效估计。第二个问题涉及估计并行数据序列/数据流中的单个或多个变化点。该计划的一部分涉及变化点的分布式计算，其中每个实体的数据序列存储在单一平台上，并且对跨平台交换数据有严格的限制。建模涉及跨各种数据序列的错位变化点，解决方案涉及具有易于处理的统计特性的计算高效方法。该议程的另一部分旨在发展更深入的理论见解，以便在存在规范模型的重尾响应变量的情况下稳健地估计变化点，并在此类问题的更复杂的化身中开发有效的方法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The project concerns two different kinds of challenges. The first challenge involves a class of regression discontinuity designs where the question is whether a treatment, like a grant, scholarship, or being accepted to a lucrative program, directly impacts the outcome, for example, the future income of the student. The difficulty is that the treatment is given precisely to those expected to have a better outcome. Hence, it is not easy to sort whether the treatment made an impact, or, simply, the better candidate got it. A standard approach uses only the data about students near the threshold, comparing those students who barely got the scholarship to those just below the threshold. The method considered in the project uses all the data. The second problem in this project concerns a situation in which the distribution of the observations changes abruptly. This can happen if, for example, there is a change in the type of infectious agent in the environment. The project's main concerns are when this change is monitored in different sites, in each of them, the change occurs at approximately the same time. However, we need to strongly constrain the amount of information passed from each site to the central control because of privacy or traffic concerns.The project deals with new estimation and inference techniques for several classes of problems that exhibit uni- or multi-dimensional discontinuities as key features of interest. The studied problems present two different kinds of challenges: The first is determining whether there is a tangible treatment effect in a class of regression discontinuity design (RDD) models, where the treatment group is determined by a pre-fixed threshold value of a core covariate. The model will be addressed via a novel point of view that introduces new estimating equations allowing the statistician to take advantage of the entire data at hand to propose semiparametric efficient estimates of the treatment effect in the presence of endogeneity. The second problem involves estimating single or multiple change-points in parallel data sequences/data-streams. Part of this plan deals with distributed computing for change-points, where the data sequence for each entity is stored on a single platform, and one has hard constraints on exchanging data across platforms. The modeling involves misaligned change points across the various data sequences, and the solutions involve computationally efficient methods with tractable statistical properties. The other part of this agenda aims to develop deeper theoretical insights into robust estimation of change-points in the presence of heavy-tailed response variables for canonical models and to develop effective methodologies in more complex incarnations of such problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.