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Projects of the German Research Foundation

The German Research Foundation (DFG) recently approved two more projects. The respective chairs of Econometrics and Statistics of Prof. Dr. Demetrescu and Business and Social Statistics of Prof. Dr. Jentsch present their newly approved projects.

The research of the Chair Business and Social Statistics in this DFG project is focused on network inference. The aim of the project is to develop new models for network data and statistical methods for estimation, validation and inference. To this end, the Chair is collaborating with researchers from Leipzig University.

The Chair of Econometrics and Statistics is working on a DFG project dealing with the significance of systemic risks and their predictions.

The aim of the project is the development of robust forecasting methods for selected measures of systemic risk and the reliable identification of risk drivers. Researchers from the University of Duisburg-Essen are cooperation partners in this project.

The research projects and their relevance are explained in more detail below.

DFG Project: Network Inference

The statistical analysis of network data plays an important role in many areas, including economics and the social sciences. Many statistical and probabilistic aspects have already been discussed in classical textbooks and have been an active field of research ever since. There are two difficulties in particular that make asymptotic analyses more difficult compared to classical data sets: The connections in the network induce statistical dependencies and typically only a single network is observed. These problems occur in many places, but are particularly problematic when it comes to estimation, (bootstrap) inference and model diagnostics. In our proposal, we aim to address these problems by utilizing the idea of local dependency structures: Nodes that are "far apart from each other" in the network can be considered independent.

We study inference in models for random networks with node attributes.

This allows, for example, the modeling of interactions of people connected via social media, while considering their workplace. In a first step, we investigate non-parametric and parametric estimation in a new graphon model suitable for this type of data. In particular, we are looking to avoid computationally intensive discrete optimization while still achieving good convergence rates. We then consider different bootstrap methods for networks. The first method is based on our new Graphon model and allows the joint resampling of network and node attributes. The second method uses the idea of local dependency to extend the block bootstrap for networks by relinking newly sampled subgraphs in a similar way to the configuration model. We study bootstrap consistency of both methods in different situations. Such results are essential for the development of inference methods. We also study goodness-of-fit tests for graphon models and online monitoring methods for dynamic networks based on the aforementioned graphon models.

Finally, we investigate the estimation of counter-factual treatment effects in observational studies with network interference for interventions that change the network structure. Here we want to allow for so-called spillover and peer effects and avoid the usual assumption of independent clusters.

Two things are particularly important to us during the work on all aspects of this project: firstly, we aim to develop a rigorous mathematical theory, and secondly, we plan to write software packages for our new models. This will allow applied scientists to apply our methods to their data, but our results can also serve as a starting point for the theoretical analysis of related models.

DFG Project: Systemic Risks

Constantly recurring financial crises illustrate the importance of systemic risks and their prediction. In a first step, the project will propose new forecasting models for systemic risk measures. The selection of suitable predictors is of particular importance. Predictors proposed in the literature include inflation, 10-year government bond yields and stock market volatility. However, many of these explanatory variables exhibit varying degrees of dependence over time. As a result, significance tests for the predictive content of these variables do not hold size, such that a selection of suitable statistically significant predictors becomes impossible. Therefore, in a second step of the project, procedures are to be developed that can handle predictors with varying degrees of dependence. This should enable a statistically sound selection of predictors for systemic risk. The third step then sheds light on the role of breaks in the variance (i.e., the range of

variation) of the explanatory variables on the statistically valid selection of predictors. Such breaks in variation are often observed for economic variables (such as inflation mentioned above) and are therefore an empirically relevant phenomenon. Therefore, it is of interest to "robustify" the significance tests for the predictors also against breaks in variance, which is the task of the third part of the project.