Nonparametric Estimation and Inference with Network Data

Princeton University, Princeton NJ

Investigators

Abstract

Network data is ubiquitous in the statistical, social, behavioral, and biomedical sciences. This type of dependent data captures interactions between the units of study, such as output between firms, trade between countries, or fundraising between politicians. Network-based information is widely used nowadays for both testing domain-specific hypotheses and policy-making decisions in data and decision sciences. However, the remarkable proliferation of network data in empirical work has not been accompanied by a complete development of statistical methods guiding its correct use and providing valid estimation and inference procedures. Current practice employing network data is limited by the few results available in the literature, and many estimation and inference problems of practical importance remain unresolved. In this project, the investigators seek to undertake a comprehensive study of non-parametric and semi-parametric statistical methods employing dyadic data, data indexed by pairs of units such as trade between two countries. The established methods and theory will serve as a building block for the analysis of more general network data. The investigators plan to develop general-purpose software to implement the main theoretical and methodological results. The project will provide training opportunities for graduate students. The research will focus on non-parametric and semi-parametric estimation and inference methods employing dyadic network data, which poses specific technical challenges due to its inherent lack of statistical independence. The project's ultimate goal is to develop comprehensive large-sample approximations leading to optimal and/or robust point estimation and statistical inference procedures for functional estimation, covering density and regression functions as special cases. To this end, the investigators will develop novel strong approximation results for stochastic processes, which will then be deployed to approximate the distribution of functional statistics based on dyadic network data. Minimax optimal uniform convergence rates for different non-/semi-parametric estimators using network data will also be established. The main theoretical results will then be applied to semiparametric estimation relying on network data. 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.