Extra Seminar Mathematics - Dr. F. Otto-Sobotka

Title: Semiparametric Distributional Regression

Abstract:
While a simple mean regression attempts to describe the expectation of a response as a function of the covariates, the results of a distributional regression offer a much broader view.
In principle, a dense set of quantiles or expectiles allows for an analysis of the complete conditional distribution of the response in a similar way as a generalized additive model for location, scale and shape (GAMLSS).
The latter combines regression predictors for each parameter of the response‘s distribution. This can lead to new insight into the dependency between the response and its covariates. In my work, I extend quantile regression to additive regression models with nonlinear as well as spatial effects. Models of this flexibility are previously unavailable to frequentist quantile regression. I achieve the inclusion of B-splines and Markov random fields, for example, with their mixed model representation and a LASSO penalty.