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，或被接受到一个有利可图的项目，直接影响结果，例如，学生的未来收入。困难之处在于，这种治疗恰恰是针对那些预期会有更好结果的人。因此，很难判断是这种待遇产生了影响，还是更优秀的候选人得到了影响。一种标准的方法只使用接近临界值的学生的数据，将那些勉强获得奖学金的学生与刚刚低于临界值的学生进行比较。项目中考虑的方法使用所有数据。这个项目的第二个问题涉及到观测分布突然变化的情况。例如，如果环境中感染因子的类型发生变化，就会发生这种情况。项目主要关注的是，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，由于隐私或流量问题，我们需要严格限制从每个站点传递到中央控制的信息量。该项目涉及新的估计和推理技术，用于几类问题，这些问题表现出一维或多维不连续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：首先是确定在一类回归不连续设计（RDD）模型中是否存在切实的治疗效果，其中治疗组由核心协变量的预先固定阈值确定。该模型将通过一种新的观点来解决，该观点引入了新的估计方程，允许统计学家利用手头的全部数据，在存在内生性的情况下提出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更改点。该计划的一部分处理更改点的分布式计算，其中每个实体的数据序列存储在单个平台上，并且对跨平台交换数据有硬性约束。建模涉及跨各种数据序列的不对齐的更改点，解决方案涉及具有易于处理的统计特性的计算效率方法。该议程的另一部分旨在对规范模型中存在重尾响应变量的变化点的稳健估计发展更深入的理论见解，并在此类问题的更复杂的体现中开发有效的方法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.