Regularisation and Qualitative Assumptions in Multivariate Density Estimation

本项目的第一个目标是更深入地了解对数凹密度估计，无论是独立的，同分布的数据，以及分箱或删失数据，特别强调全局一致性和尾部行为。这种强形状约束的松弛也将被研究。此外，我们正计划扩展我们以前的工作在多变量和回归设置的对数凹分布。这些扩展包括分箱和审查数据，分类应用程序，以及反卷积问题。我们的一些方法是由该项目的劳动力市场数据和荧光显微镜的问题驱动的，并将应用于这些数据。

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.