Regularisation and Qualitative Assumptions in Multivariate Density Estimation

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A first goal of the present project is a deeper understanding of log-concave density estimation, both for independent, identically distributed data as well as binned or censored data, with particular emphasis on global consistency and tail behavior. Relaxations of this strong shape-constraint will be investigated as well. Further we are planning to extend our previous work on log-concave distributions in multivariate and regression settings. These extensions include binned and censored data, applications to classification, and deconvolution problems. Some of our methods are driven by, and will be applied to, labour market data from the project and problems from fluorescence microscopy.