FOR 916:  Statistical Regularisation and Qualitative Constraints - Inference, Algorithms, Asymptotics and Applications

• Subject Area: Mathematics ; Humanities ; Social and Behavioural Sciences
• Term: from 2008 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 40095828

A central challenge at the interface of statistics and various branches of science is the development of methods for large data sets, complex data structures and high dimensional predictors. The aim of this Swiss German Research Unit is the development and investigation of new statistical procedures (statistical regularisation methods) for complex data structures as they appear in many areas of application.
Our major focus will be on methods, which result from qualitative constraints on the structure and geometry of the data model. Our fundamental claim is that statistical regularisation by qualitative constraints represents an unifying method for modelling of data structures, which is, on the one hand, flexible enough to recover important features of data and, on the other hand, specific enough to control the prediction or classification error.
Each of the fourteen subprojects deals with specific aspects of this goal. In cooperation with members of the Research Unit and with external partners specific areas of application will be tackled. This includes problems from systems biology, medical event analysis, astrophysics, material science, atmospheric research, forest science, labour market policy, biophotonics, medical imaging and empirical economic research.
These apparently different topics will be treated from the unifying perspective of statistical regularisation. In all of these disciplines statistical methods have been developed rapidly during the last years and only recently surprising commonalities become visible. Although these areas seem to be different at a first glance: The researchers expect that the common mathematical language and statistical methods will allow discovering further hidden commonalities. Therefore, the Research Unit is interdisciplinary, consisting of statisticians, mathematicians, computer scientists and economists, who collaborate closely.

• DFG Programme: Research Units
• International Connection: Austria, Switzerland

Projects

• Administration/Data Management (Applicant Munk, Axel )
• Complex Nonparametric Models (Applicant Mammen, Enno )
• Estimation of Variograms by Monotone, Conditionally Negative Definite Functions with Applications in Forestry (Applicant Schlather, Martin )
• Honest Confidence Sets for Sparsely and Non-Sparsely Tuned Model Selection Estimators (Applicant Schneider, Ulrike )
• Inference for Semimartingale Stochastic Volatility Models (Applicant Woerner, Jeannette H. C. )
• Nonlinear Inverse Problems with Noisy Operators (Applicant Hohage, Thorsten )
• Nonparametric Identification and Inference in Duration Analysis (Applicant van den Berg, Gerard J. )
• Partial least squares for serially dependent data (Applicant Krivobokova, Tatyana )
• Quantifying Confidence for Computer-Intensive Classifiers (Applicant Dümbgen, Lutz )
• Regularisation and Qualitative Assumptions in Multivariate Density Estimation (Applicant Dümbgen, Lutz )
• Regularization Methods for High-Dimensional Data (Applicant van de Geer, Sara A. )
• Stability Analysis for Clustering (Applicant Buhmann, Joachim M. )
• Statistical Inference in Inverse Problems with Qualitative Prior Information (Applicant Munk, Axel )
• Statistical Modelling of Labor Market Processes in Misclassified Administrative Labor Market Data (Applicant Fitzenberger, Ph.D., Bernd )
• Statistical Multiscale Parameter Selection Strategies (Applicant Munk, Axel )
• Structure Estimation, Graphical Modelling and Causal Inference in High Dimensions (Applicant Bühlmann, Peter )
• Structured Regression Models (Applicant Zucchini, Walter )

• Participating Institution: Schweizerischer Nationalfonds (SNF)
• Spokespersons: Professor Dr. Lutz Dümbgen; Professor Dr. Axel Munk