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，以响应在早期数据收集过程中吸取的教训。在这些情况下，研究人员可能需要评估政策效果，检验假设，或随着新数据的出现而动态调整实验设计。估计方法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论。这个项目将发展新的和创新的方法来分析这种顺序统计问题。该项目将设计出易于数学解决的方法，使研究人员能够正确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。本文的研究成果将改进政策评估的方法，从而改善美国经济和治理的运行。这个项目将开发新的方法来分析动态环境中的统计决策问题。我们将扩展实验框架的限制，以纳入各种形式的顺序数据收集的信息结构。研究的第一部分将侧重于顺序设置，其中分析师可用的信息是固定的，或者是收集数据的外部设置。项目的第二部分将包括一些设置，在这些设置中，数据的顺序收集将动态地演变，以反映从数据的早期部分获得的信息。对于每一种设置，两个关键的研究成果将是：(i)新的信息适应渐近表示定理；（ii）一个新的渐近最优性框架和研究结果。本文的研究成果将改进政策评估的方法，从而改善美国经济和治理的运行。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。

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.