Collaborative Research: Honest and Robust Inference with High Dimensional Data

现代经济学和其他科学中的数据分析通常涉及研究人员对许多个体的行为进行预测或解释的情况;研究人员也可能对单个因素如何影响结果感兴趣，但必须包括其他几个因素来解释感兴趣的结果。 在这些情况下，围绕测量效果的统计不确定性测试是困难的，现有的方法没有提供精确和有效的方法来测量这种不确定性。该研究项目将开发新的和改进的方法，用于评估与这两种情况下的效果测量相关的统计不确定性。这些情况经常出现在解决许多政策问题的经济学和其他社会科学研究中，准确评估不确定性的方法对于提供良好的政策建议非常重要。本研究的成果将有助于提高政策评估和统计预测的质量，从而为政策制定者提供更好的建议。 这将有助于更好的政策结果，从而促进美国更快的经济增长。本研究项目将开发新的方法来测试在两种情况下的高维数据估计的统计不确定性。 在第一种设置中，我们开发了一种通用的方法来构建满足平均覆盖属性的区间：区间覆盖平均真实效应的预定分数（比如95%）。专注于平均覆盖率使我们能够形成自动反映数据驱动正则化效率增益的区间，包括经验贝叶斯方法和基于机器学习技术的回归函数估计器。在通常的覆盖范围概念下，这种收益是不可能的，因为在这种概念下，每种影响都需要单独的覆盖范围保证，而不仅仅是平均的覆盖范围保证。在第二种情况下，我们重点关注通常的覆盖范围概念。为了获得信息的置信区间，我们利用先验限制的大小的控制系数。我们表明，我们的建设享有几个最优性和近最优性的属性。 这项研究的结果将提高政策建议的质量，从而提高美国的经济增长率。该奖项反映了NSF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。

Modern data analysis in economics and other sciences often involves situations in which researchers are interested in making predictions about or explaining the behavior of many individuals; researchers may also be interested in how a single factor affects an outcome but have to include several other factors in explaining the outcome of interest. Testing for statistical uncertainty surrounding the measured effects in these situations is difficult and existing methods do not provide precise and efficient ways to measure this uncertainty. This research project will develop new and improved methods for accessing statistical uncertainty associated with effect measurements in both situations. These situations arise routinely in economics and other social science research that addressing many policy questions, and accurate methods for assessing uncertainty are important for providing good policy recommendations. The results of this research project will help improve the quality of policy evaluation and statistical prediction and as result, provide policy makers with better advice. This will contribute to better policy outcomes, hence foster faster economic growth in the US.This research project will develop new methods to test statistical uncertainty in high-dimension data estimation in two settings. In the first setting, we develop a general method for constructing intervals that satisfy an average coverage property: the intervals cover a prespecified fraction (95%, say) of the true effects on average. Focusing on average coverage allows us to form intervals that automatically reflect efficiency gains from data-driven regularization, including empirical Bayes methods, and estimators of a regression function based on machine learning techniques. Such gains are not possible under the usual notion of coverage, under which a coverage guarantee is required for each effect individually, not just on average. In the second setting, we focus on the usual notion of coverage. To obtain informative confidence intervals, we exploit a priori restrictions on the magnitude of the control coefficients. We show that our construction enjoys several optimality and near-optimality properties. The results of this research will improve the quality of policy advice and as a result increase the rate of economic growth in the US.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.