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

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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.