Central Project: Research Unit Structural Inference in Statistics: Adaption and Efficiency

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Because of the increasing availability of data, statistics plays a more and more prominent role in many scientific and practical areas. On the other hand, the most general realistic models are usually very complex such that poor statistical precision is very common in spite of the large amount of data. The Hamburg-Berlin-Potsdam Research Unit Structural Inference in Statistics: Adaptation and Efficiency aims at developing new methods and tools to profit from structures underlying high-dimensional complex data. Structure not only concerns the unknown targets of inference (involving smoothness, sparsity or low dimensions), but also the data structure involving unknown correlation matrices, hierarchical or multiscale interaction or support properties of the noise. The long-term goal is to establish a general framework to adapt automatically and simultaneously to different structures that might be present in the data. This will allow for much more efficient statistical procedures, which will have a strong impact on the significance of statistical results in a wide range of applications. Moreover, the gained fundamental insight will often allow a quick transfer of efficient methods to new structures in upcoming applications. The advanced new tools developed for the mathematical analysis will push on the whole field of mathematical statistics for complex structural models. The research unit comprises eight principal investigators from the University of Hamburg, Humboldt-Universität zu Berlin, Weierstraß Institute Berlin and the University of Potsdam. Their joint expertise in different areas of statistics is focussed on modern efficient methods which are analysed using advanced mathematical theory and are applicable to a wide range of practical problems. We propose six projects, each of which is jointly led by two or three principal investigators from different places. A dynamic and ambitious research collaboration is aspired within the whole research unit and in exchange with international experts.