Hybrid Methods for Statistical and Econometric Modeling

Brown University, Providence RI

Investigators

Abstract

This research project will develop statistical methods that account for the unavoidable fact that most models only represent approximations to reality, and researchers often are faced with a choice of a number of different plausible models. The project will tackle this issue along three fronts: (i) by devising a modification to the widely used method-of-moment approaches from economics and statistics that account for imperfectly measured data, (ii) by providing formal statistical methods that account for the fact that researchers typically adapt the complexity of their model based on the amount of data they have, and (iii) by developing forecasting methods that combine the predictions of multiple (possibly imperfect) models to yield more robust forecasts. To accomplish this, techniques developed in very diverse fields of study will be combined and augmented, and their advantages in contexts very different from where they initially were conceived will be leveraged. The methods to be developed generally can be applied in many areas of study that employ statistical modeling and thus could impact fields as diverse as medicine, weather forecasting, pandemic evolution predictions, climate modeling, or the evaluation of the effectiveness of social intervention programs. Graduate students will be involved in the research process, and computer programs implementing the new methods will be made publicly available. This research project will solve the problem of assigning a logical interpretation to the method of moments when the data rejects the model. The problem will be addressed by determining the minimum amount of measurement error that would be needed to reach agreement between the data and the model. This approach will draw from two currently very active areas of research, namely, empirical likelihood and optimal transport. Another part of the project will provide researchers with methods to account for their model selection process when making statistical inference by leveraging techniques from the general field of nonstandard inference. Finally, the project will exploit the largely overlooked fact that a multi-model forecasting process can be written as a model selection problem, where the model selection variables can be set-valued, thus emphasizing a connection with the so-called set-identified models, which have received considerable attention in recent years. The research will provide a natural frequentist counterpart to the commonly used Bayesian approaches to multi-model forecasts. 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.