Network Inference: Nonparametric estimation, bootstrap, and model diagnostics in sparse graphon models with vertex attributes

• Applicants: Professor Dr. Carsten Jentsch; Dr. Alexander Kreiß
• Subject Area: Statistics and Econometrics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 534099487

Statistical network analysis plays an important role in economics and social sciences as well as other research fields. In classical textbooks, many statistical and probabilistic aspects were discussed, and the statistical analysis of networks has been an active area of research since then. The main difficulties arise from the relational structure of networks which induces dependence, and from the fact that typically only one single network is observed. Asymptotic theory is therefore a greater challenge compared to classical data setups. This is true for many statistical tasks, but holds in particular when it comes to estimation, (bootstrap) inference, and model diagnostics. In this proposal, we tackle these problems by adopting a local dependence viewpoint: what happens “far apart” in the network may be treated as independent, and strong dependence appears only locally. We will address inference problems in models for network data with vertex attributes, which allows, e.g., to model interactions of people connected by social media with information about their workplace. We focus on models in which the networks are random. Our first specific goal is to develop a new graphon model which is suitable for modeling networks together with vertex attributes and study nonparametric as well as parametric estimation in this model. A focus in the estimation will be to avoid expensive discrete optimization and to achieve good convergence rates. Then, we study different bootstrap methods for networks. While the first bootstrap will be based on the new graphon model and allows the simultaneous resampling of a network together with vertex attributes, the second bootstrap under consideration is a block-type bootstrap for networks that borrows ideas from the configuration model to rewire the resampled sub-graphs, exploiting the idea of local dependence. We will study bootstrap consistency of both methods under various scenarios. Such results are crucial to develop valid inference methods. In particular, we will also study goodness-of-fit testing for graphon-type network models. We will consider online monitoring procedures for dynamic networks based on the previously mentioned graphon models. Finally, we are concerned with the estimation of counter-factual treatment effects from observational data with network interference. Hereby, we allow for peer and spill-over effects and focus on interventions that change the network structure, e.g., a lockdown, and we aim to avoid the often-made assumption of clustered interference or independent clusters. Throughout all workpackages of this project, we focus on two aspects: Firstly, developing rigorous theory and, secondly, providing accessible results and software for the specific models under consideration. On the one hand, this enables applied researchers to directly apply our methods to their data. On the other hand, our results can be used as starting point for further theoretical analysis in related models.

• DFG Programme: Research Grants