Collaborative Research: Robust Inference for Kernel Smoothing and Related Problems

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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.