Methodology for Qualitative Constraints in Semi-Parametric Models

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

Qualitative constraints such as concavity (law of diminishing returns) are ubiquitous in social sciences and economics. In order to incorporate these important constraints into statistical modeling, users often resort to simpler models, for example, linear regression. However, these simpler models are inflexible and cannot fully explain complex scientific phenomena. In turn, semi-parametric models provide necessary flexibility and interpretability. However, in fitting these semi-parametric models, qualitative constraints are often left unexploited. Ignoring these constraints, will not only lead to a loss in interpretability but also forgo some accuracy in the performance of the estimates. The broad goal of this proposal is to develop new statistical methods that respect subject matter qualitative constraints and make such methods more accessible to researchers via open-source software implementation. This project has three main aims: (1) to develop general non-parametric regression estimators that account for available subject matter constraints and adapt to the smoothness of the underlying truth; (2) to explore systematic approaches for semi-parametric estimators that incorporate naturally occurring shape constraints on the nuisance components; and (3) to assess improved doubly robust estimators of functionals that can be represented in terms of variationally dependent nuisance parameters, whose relationship is shape-constrained on a subject matter basis. This in return would allow for significant improvement of estimation accuracy, thereby outperforming the existing tools that do not incorporate such information. The results of the project will find utility in addressing the interpretability and reproducibility concerns that have recently emerged in a broad range of domain knowledge disciplines, from social sciences to economics to epidemiology. The project will offer a multitude of opportunities for research training and professional development of the next generation of statisticians and will also engage in bolstering diversity in statistical sciences. 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.