### Workgroup "Quantile regression"

**Head of workgroup:** Prof. Dr. Holger Dette**Members:**

- Ria Van Hecke

**Description:**

A central aim of statistics is the quantification of the dependence between covariates and dependent variables. For example, one might be interested in the influence of age on the height of a person. One possibility to analyse such dependencies is to consider the mean height at a given age. This approach is also known as mean regression. In many cases, further aspects of the conditional distribution of heights, as for example 'typical' heights at a given age are of interest. An elegant way to describe such connections is provided by the method of quantile regression. Mathematically, the aim is to construct curves that divide the data in two regions with a given portion of data above/below the corresponding curve. Such an approach allows to identify 'atypically' high/low response values.

The aims of the work group are several-fold. One core theme is the development of estimation procedures that are applicable in general non-parametric settings and yield non-crossing quantile curves. Those estimators are used to conduct inference about the underlying data structure. Further areas of research include the extension of quantile regression estimators to new settings such as censored data, multidimensional response variables and robust estimation procedures for time series.