A Design-based Riesz Representation Estimation Approach for Randomized Experiments

This research project will develop and investigate methods for the estimation of causal effects in randomized experiments. Randomized experiments are used as an empirical method by scientists and researchers in a wide range of fields, both in the public and private sectors. The method is appreciated by researchers because it allows for conclusions that are credible and robust. However, randomized experiments cannot be used to investigate complex settings, such as when study participants interact with each other, because estimation methods and theory are lacking. The project will address this gap by developing new estimators that can be used in complex experiments. The methods to be developed will allow scientists and researchers to investigate new and more intricate questions, ultimately advancing our understanding of both the social and medical sciences. In addition, graduate students will be mentored, and publicly available, open-source software will be developed. A central feature of this research project, which sets it apart from previous work in this context, is the development of a general framework and theory that will encompass most empirical settings in the relevant fields. The framework will cover both settings with interference, including spillover effects and network experiments, and complex experimental designs. This will be achieved by re-interpreting and understanding the empirical problem as a problem within the mathematical subdiscipline of functional analysis. Initial results indicate that the Riesz representation theorem from functional analysis can be used as the basis for a general approach to construct estimators for complex experiments. The project will investigate and develop this approach to a full-fledged estimation procedure and associated statistical theory. In addition to the core framework and theory, the project also will develop variants of the estimators that can accommodate high-dimensional models and adjustments based on background information. Methods for inference and uncertainty characterizations will be developed in the form of variance estimators and central limit theorems, allowing researchers to construct hypothesis tests and confidence intervals to gauge the statistical uncertainty in their investigations.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.