Regression models make up a large part of the standard tools for empirical analyses in many areas of scientific research. Classical ordinary least squares regression or even generalized linear models aim for the explanation of changes in the conditional mean of a response variable. However, in the past years we could observe an increasing interest for models that help to analyze more general aspects of a response's distribution (called distributional regression models).

This model class contains nonparametric methods like quantile and expectile regression as well as flexible parametric approaches like Generalized regression models for location, scale and shape. These allow for modeling of the complete conditional distribution of the response, either through a set of quantiles / expectiles or through a highly fittable distribution family. All of them can incorporate more flexible configurations of covariates such as nonlinear or spatial effects with appropriate penalties.

The scope of this project is to further develop different classes of distributional regression and derive suitable techniques for statistical inference. The visited classes range from different approaches towards quantile and expectile regression to mode regression and generalised additive models for location, scale and shape (GAMLSS). We also aim to apply these procedures to solve real-world empirical questions.

The project is centered at the University of Göttingen and is conducted in cooperation with the chair for statistics of Thomas Kneib.

• Sobotka, F., Kauermann, G., Schulze Waltrup, L. und Kneib, T. (2013) On confidence intervals for semiparametric expectile regression. Statistics and Computing, 23(2), 135-148.
• Sobotka, F., Marra, G., Radice, R. und Kneib, T. (2013) Estimating the relationship between women’s education and fertility in Botswana by using an instrumental variable approach to semiparametric expectile regression. Journal of the Royal Statistical Society: Series C (Applied Statistics), 62(1), 25-45.
• Kneib, T. (2013) Beyond Mean Regression (with discussion and rejoinder). Statistical Modelling, 13, 275-385.
• Schulze Waltrup, L., Sobotka, F., Kneib, T. and Kauermann, G. (2015) Expectile and Quantile Regression – David and Goliath? Statistical Modelling, doi:10.1177/1471082X14561155.

• Sobotka, F., Mirkov, R., Hofner, B., Eilers, P. und Kneib, T. Modeling Flow in Gas Transmission networks using Shape-constrained Expectile Regression. European Conference on Operational Research (EURO 2012), Vilnius, 8. - 11.7.2012
• Sobotka, F., Salvati, N., Ranalli, G. und Kneib, T. Adaptive Semiparametric M-Quantile Regression. 3. gemeinsame Arbeitstagung der Deutschen Arbeitsgemeinschaft Statistik (DAGStat 2013) Freiburg, 18.-23.3.2013
• Kneib, T. Beyond mean regression. International Workshop on Statistical Modeling (IWSM) 2012, Prag, 16.-20.7.2012
• Sobotka, F., Mayr, A. und Kneib, T. Fractile Boosting: a Novel Approach towards Mode Regression. International Workshop on Statistical Modeling (IWSM) 2013, Palermo, 8.-12.7.2013
• Sobotka, F. und Kneib, T. SPQR: semiparametric quantile regression. International Workshop on Statistical Modeling (IWSM) 2014, Göttingen, 11.-14.7.2014