Collaborative Research: Robust Inference for Kernel Smoothing and Related Problems

经济学、公共政策和其他相关学科的研究，以及基于证据的政策制定决策，都需要准确有效的测量。有效的测量需要准确、简单和灵活的统计方法，这些方法可以很容易地从数据中得出结论。这些方法在大数据、高速计算和机器学习的现代时代变得越来越重要。分析经济问题的新统计方法，包括现代机器学习和类似的数据科学方法，在经济理论中很受欢迎，因为它们通常在测量的灵活性和简单性之间提供了很好的折衷，但它们并不总是可信的，因为结果往往取决于这些方法的实施方式。这项研究将开发新的方法，说明如何在实施中做出的选择影响研究人员获得的结果。提出的研究为分析大型和复杂的数据集提供了新的、现代的统计和计量经济学方法。这些方法产生的结果不依赖于模型如何实现的具体细节。这项研究将产生更可信的实证结果，从而改进决策建议。这项研究解决了经济分析方法论中的一个基本问题，对经济科学做出了重要贡献，增强了美国在经济科学领域的全球领导地位。研究结果将为政策研究提供更好的方法，从而提高经济政策的制定。因此，由于更好的政策，这项研究有可能促进美国的经济增长。这个研究项目的重点是一类非参数或半参数估计器，称为平滑成对估计器，以及其推广，并寻求开发新的大样本近似，产生比现有估计器更健壮的统计过程。平滑两两估计器的这些更一般的分布近似明确地捕获了调优参数选择的效果，提供了对标准结果的改进，因为它们包含了当前文献中可用的发现，同时也突出了以前假设的新特征和问题。该研究项目有三个主要部分：(i)光滑两两估计的广义分布近似，导致高斯和非高斯极限分布，（ii）具有可证明的优越鲁棒性的分析和基于自举的推理方法，以及（iii）有效的高阶展开，正式表明所提出的广义分布近似和相关鲁棒推理方法比现有方法有明显的改进。研究结果将为政策研究提供更好的方法，从而提高经济政策的制定。因此，由于更好的政策，这项研究有可能促进美国的经济增长。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。

Research in economics, public policy, and other related disciplines, as well as evidence-based policy-making decisions require accurate and efficient measurements. Efficient measurements require accurate, simple, and flexible statistical methods that can be easily implemented to draw conclusions from data. These methods are becoming increasingly important in the modern era of big data, high-speed computing and machine learning. New statistical methods for analyzing economic problems, including modern machine learning and similar data science approaches, are popular in economic theory because they usually offer a good compromise between flexibility and simplicity in measurement, but they are not always trusted because the results often depend on how these methods are implemented. This research will develop new methods that account for how the choices made in implementation affect the results obtained by the researcher. The proposed research offers new, modern statistical and econometric methods for analyzing large and complex data sets. These methods will produce results that do not depend on the specific details underlying how the models are implemented. This research will lead to more credible empirical findings and hence improve policy-making recommendations. This research tackles a fundamental question in the methodology of economic analyses and makes important contribution to economic science, enhancing US global leadership in economic science. The results of this research project will lead to better methods for policy research, hence enhance economic policy making. The research therefore has the potential to enhance US economic growth because of better policies.This research project focuses on a class of non- or semi-parametric estimators known as smoothed pairwise estimators, as well as generalizations thereof, and seeks to develop new large-sample approximations that produce statistical procedures that are more robust to the specifics of their implementation than existing estimators. These more general distributional approximations for smoothed pairwise estimators explicitly capture the effect of tuning parameter choices, offering improvements over standard results because they encompass findings currently available in the literature while also highlighting new features and problems previously assumed away. The research project has three main parts: (i) generalized distributional approximations for smoothed pairwise estimators, leading to both Gaussian and non-Gaussian limiting distributions, (ii) analytic and bootstrap-based inference methods with demonstrable superior robustness properties, and (iii) valid higher-order expansions showing formally that the proposed generalized distributional approximations and related robust inference methods give demonstrable improvements over existing methods. The results of this research project will lead to better methods for policy research, hence enhance economic policy making. The research therefore has the potential to enhance US economic growth because of better policies.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.