Study of dependencies and post-selection inference for contemporary data structures

Contemporary data structures include multidimensional/multivariate data of different nature; data as numbers, curves, surfaces/images, graphs, and circular data. Flexible models are needed to adequately describe such data. This projects focusses on two domains of statistical inference methods for the model parameters (finite or infinite-dimensional). First, a study of the complex dependence structures in the data, developing copula-like concepts. Different tools for dependence modelling are needed, depending on the data structures (e.g. graphical or circular). Inherent herein is the choice of a copula model and the marginal distributions. Second, since a first inference step often involves selecting a model among a set of plausible models, statistical inference for the parameters in the selected model should take into account the stochastic nature of any model selection step. This post-selection inference issue is crucial for valid statistical inference tools and will be further developed for state-of-the art modelling efforts.

Keywords:Dependency, Post-selection inference, Flexible modelling, Multivariate data, Copulas

Disciplines:Statistics