Collaborative Research: Honest and Robust Inference with High Dimensional Data

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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.