Dependencies, including copula-based flexible modelling and applications

This doctoral research will contribute to the study of dependencies, with the aim to improve statistical analysis by taking into account dependencies in an appropriate way. A first well-known way to express the dependence of a (or more) variable(s) on a variable of interest is by regression models.  Another general approach to describe dependency between random variables (or even random vectors) is by using copula modelling. For example, when considering a portfolio of assets, the dependence between the assets plays an important role when, for example, appropriately measuring and evaluating the risk of a portfolio. A first step in this is then to study risk measures as such, and discussing statistical inference for these. Next, a risk of a portfolio is measured and its evaluation depends on the dependence structure between the assets. A first part of the doctoral research will look into risk measures and applications. In multiple regression models for example, the possible dependence between error structures might be modelled adequately via a copula. Part of the doctoral research might be devoted to the study of flexible regression modelling. Although the use of copulas is very appealing, there are important aspects of it, such as the choice of the dependence structure, that need to be addressed. When this choice is data-driven, that part of the process needs to be taken into account in statistical inference issues. Further, dependencies have been studied mainly for continuous real-valued random variables, whereas data can be discrete, can take values in function spaces, a simplex, …, to give a few examples. This doctoral research will contribute to the study of dependencies, in some of its many aspects, while keeping an eye on flexible enough modelling that allows to capture complexity of contemporary data structures.