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，以及基于证据的决策决策，都需要准确和有效的衡量标准。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实施，以便从数据中得出结论。在大数据、高速计算和机器学习的现代时代，这些方法变得越来越重要。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一个很好的折衷，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来解释在实施过程中做出的选择如何影响研究人员获得的结果。拟议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。这些方法将产生不依赖于模型如何实现的具体细节的结果。这项研究将导致更可信的实证结果，从而改进政策制定建议。这项研究解决了经济分析方法论中的一个基本问题，并对经济科学做出了重要贡献，加强了美国在经济科学领域的全球领导地位。这一研究项目的成果将为政策研究提供更好的方法，从而促进经济政策的制定。因此，由于更好的政策，这项研究具有促进美国经济增长的潜力。本研究项目专注于一类称为平滑成对估计的非或半参数估计及其推广，并试图开发新的大样本近似，其产生的统计过程对其实施的细节比现有估计更稳健。这些更一般的平滑成对估计的分布近似明确地捕捉了调整参数选择的影响，提供了比标准结果更好的结果，因为它们包含了目前文献中可用的发现，同时还突出了以前假设的新特征和问题。该研究项目包括三个主要部分：(I)光滑两两估计的广义分布近似，得到高斯和非高斯极限分布；(Ii)分析和基于Bootstrap的推理方法，具有明显的优越稳健性；(Iii)有效的高阶展开，形式上表明所提出的广义分布近似和相关的稳健推理方法比现有方法具有明显的改进。这一研究项目的成果将为政策研究提供更好的方法，从而促进经济政策的制定。因此，这项研究有可能因为更好的政策而促进美国的经济增长。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。

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.