Collaborative Research: Asymptotic Approximations for Sequential Decision Problems in Econometrics

经济和社会数据通常是随着时间的推移而收集的。有时可以调整数据收集方法，以适应早期数据收集过程中吸取的经验教训。在这些情况下，研究人员可能需要估计政策效果，测试假设，或随着新数据的出现而动态调整实验设计。估计方法将需要随着数据的变化而调整。目前还没有有效的方法来从以这种顺序方式收集的数据中得出推断。这个项目将开发新的和创新的方法来分析这种序贯统计问题。该项目将设计出易于数学求解的方法，使研究人员能够适当评估动态收集的数据，并最大限度地提高数据用于得出政策结论的效率。这些方法将在经济学、生物统计学、医学和其他社会科学的几个领域有用。这项研究的结果将改进政策评估的方法，从而改善美国经济和政府的运作。该项目将为分析动态环境下的统计决策问题开发新的方法。我们将扩大实验框架的限制，将信息结构纳入各种形式的顺序数据收集。研究的第一部分将重点放在顺序设置上，在顺序设置中，分析师可以获得的信息是固定的或以外在方式设置为收集的数据。该项目的第二部分将包括数据顺序收集动态演变的设置，以反映从数据的较早部分获得的信息。对于这些背景中的每一个，两个关键的研究产出将是：(I)新的适应信息的渐近表示定理；和(Ii)新的渐近最优框架和发现。这项研究的结果将改进政策评估的方法，从而改善美国经济和政府的运作。这一奖项反映了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。

Economic and social data are often collected over time. The data collection method may sometimes be adjusted to respond to lessons learnt during the data collection in earlier periods. In these situations, researchers may need to estimate policy effects, test hypotheses, or adjust experimental designs dynamically as new data become available. The estimation method will need to adjust as the data changes. There are currently no efficient methods for drawing inference from data collected in such sequential manner. This project will develop new and innovative methods for analyzing such sequential statistical problems. The project will devise methods that are easy to solve mathematically and allow researchers to properly evaluate dynamically collected data and maximize the efficiency with which the data is used to draw policy conclusions. These methods will be useful in several areas of economics, biostatistics, medicine, and other social sciences. The results of this research will improve methods of policy evaluation, hence improve the functioning of the US economy and governance.This project will develop new methods for analyzing statistical decision problem in dynamic settings. We will extend the limits of experiments framework to incorporate the informational structure in various forms of sequential data collection. The first part of the research will focus on sequential settings where the information available to the analyst is fixed or set exogenously to the collected data. The second part of the project will include settings where sequential collection of data evolves dynamically to reflect information gained from earlier portions of the data. For each of these settings, two key research outputs will be: (i) new information-adapted asymptotic representation theorems; and (ii) a new asymptotic optimality framework and findings. The results of this research will improve methods of policy evaluation, hence improve the functioning of the US economy and governance.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.